BHUTANESE STUDENTS’ ABILITY TO APPLY THE CONCEPTS OF LIGHT
REFLECTION AND REFRACTION TO THE SITUATIONS RELATED TO A FISH
TANK
Sushmika Tamang1,*, Suchai Nopparatjamjomras2, 3,# Thasaneeya R.
Nopparatjamjomras2,#
1
MSc. in Science and Technology Education. Institute for Innovative Learning, Mahidol
University. Thailand
2
Institute for Innovative Learning, Mahidol University. Thailand
3
Department of Physics, Faculty of Science, Mahidol University. Thailand
*e-mail: sush_tamang@yahoo.com, #e-mail: suchai.nop@mahidol.ac.th
Abstract
This study aims to identify the grade 10 Bhutanese students’ ability to apply the concepts
about reflection and refraction of light, and total internal reflection in the situations related to a
fish tank. For this purpose, an open-ended questionnaire consisting of 4 real life situations related
to a fish tank was created. The questionnaire was piloted with 45 grade 10 Bhutanese students.
The responses were used to develop the 8-multiple choice questions on light refraction and
reflection named as Light Reflection and Refraction Test (LRRT). The test consists of 2 different
situations which are the application of the reflection and refraction of light, and total internal
reflection concepts. The content validity of the test was validated by three physics researchers.
This test then was administered to 111 grade 10 Bhutanese students from 3 secondary schools in
Thimphu, Bhutan. The result showed that most of the students could not apply the related
physics concepts to the 2 fish tank situations. In addition, some important and prevalent
misconceptions were also revealed by this study. It indicates that students require practical
application of the optics concepts if they have to deeply understand the concepts taught and
apply in real life situations.
Key-Words: Misconceptions, Reflection, Refraction, Total Internal Reflection, Fish Tank
Introduction
Bhutanese students completing grade 10 have been taught the concepts of light refraction
and reflection, and their applications i.e., image formed by a plane mirror, characteristics of the
image by simple ray diagram, regular and irregular reflection, image formed by a pair of parallel
and perpendicular plane mirrors and simple periscope, refraction of light through a glass block
and a triangular prism, qualitative treatment of simple applications with calculation such as real
and apparent depth of objects in water, apparent bending of sticks in water, total internal
reflection, critical angle and conditions for total internal reflection, twinkling of stars, appearance
of the sun, mirage formation, and sparkling of diamond. Therefore, the students are expected to
be able to apply these concepts in different optical phenomena that occur around them. With the
objective of checking the students’ ability to apply the concepts of optics, researchers have
developed a relevant test called Light Reflection and Refraction Test (LRRT). Surprisingly, the
students’ responses to this test showed that most of them could not apply the relevant optics
concepts to the situations related to a fish tank. Moreover, our research findings indicated that
students had misconceptions about how light propagates through different media, how the
objects are seen due to reflection and how the colors of different objects are perceived.
There are other similar research findings in other countries about students’
misconceptions in optics (1-9). Moreover, a significant finding of many research studies is that
the students' ideas of the world are often formed before any formal instruction and are often quite
different from scientifically accepted ideas (9-10). Furthermore, it has been observed that
teaching students without clearing their misconceptions significantly reduce their understanding
which further lessens their ability to function effectively in applying the concepts learnt (10).
The poor performance of the students in the test might be because of the fact that the
assessment of students’ learning in Bhutan is mainly summative in the form of examination; the
assessment questions at the end of each chapter in physics text books of grades 9 and 10 (11-12)
and the questions framed in the exams, predominantly focus on factual recall with minimum
assessment of skills and scientific values. Hence, the science learning in these grades is mostly
about learning facts and figure and does not pose much cognitive challenge to the students. This
has been proved in a study conducted for a need assessment of science education in Bhutan in
2008. Firstly, it was found that science students who graduated from grade 12 lacked basic level
knowledge and important practical skills. Secondly, it was felt that the curriculum in science did
not make full use of the natural resources and examples available in Bhutan (13).
Therefore, there is an urgent need to work for improvement of the assessment process.
The development of the LRRT might be a small step towards improving the assessment process.
Therefore, this paper will present a development of the LRRT and the analysis of students’
response to the test.
Methodology
The test was implemented on 111 Bhutanese students of grade 10 from three secondary
schools in Thimphu which is the capital city of Bhutan. All the students had previously studied
the concepts of reflection and refraction of light and total internal reflection in grades 9 and 10.
Throughout Bhutan, the physics curriculum and text books are uniform for each grade. The
students in the three schools were taught by using traditional approach and hence had no
experience of doing hands-on laboratory experiments on these topics.
There are so many scenarios going on around the world which is due to light reflection
and refraction, and total internal reflection. These scenarios happen every day but they are
insignificant to be noticed. One of such scenario is the fish tank scenario. Applications of light
reflection and refraction, and total internal reflection that can be observed in a fish tank were
considered to develop the multiple item test. However, to generate the distractors, open-ended
items were developed initially as Haladyna, Downing and Rodriguez stated that effective items
can be created only after exhaustive interviews or through open-ended tests (14). Open-ended
items consisting of 4 real life situations related to a fish tank were developed after thorough
review of prior research into students’ understanding of light reflection and refraction, and total
internal reflection (15-19), Bhutanese curriculum and syllabi (20), and the combined teaching
experience of the researchers. These open-ended items were administered on 45 students of
grade 10 in Thimphu, Bhutan who had studied the concepts of light reflection and refraction, and
total internal reflection. The responses gathered from these students were used to develop the
distractors for multiple-choice items taking into consideration the frequency of similar responses.
To explore the content validity, the test was reviewed by a team of experts who checked
the relevance of the content with respect to the intended test population secondary school
students. Their consensus on the correct answer to each item was also taken into account. The
experts were in agreement which provided a satisfactory content validation result.
Finally, there are 2 situations in the LRRT. The first situation consists of 5 questions
which are about the fish tank kept on top of a white paper as shown in Figure 1. For the first 3
questions, the tank is half filled with water. Students have to choose the correct response from
the 4 options provided with reasons. Students are asked to give the colors of the 1) base and four
walls of the fish tank 2) above and 3) below the water level when viewed from the top. For the
last 2 questions, the tank is completely filled. Students have to choose the correct options for the
colors of 4) the walls and 5) the base when they observe from vertically above the fish tank in
this condition.
For the second situation, the three sides wall of the fish tank are covered with yellow
colored papers and one side wall is left uncovered. The tank is kept on a blue colored paper and
half-filled with water as shown in Figure 2. Unlike the first situation, the second situation
consists of only 3 questions. Students have to choose the correct response from the 6 options
provided with reasons. The difference in the number of options in the first and second situations
is mainly because there was more variety of reasons provided by the students in the second
situation of the open-ended test. Although most standard forms of test have spaces for five
response choices, there is no conventional rule of test construction theory that requires five
choices to be provided (21). Similar to the first situation, in the second situation also, students
are asked to give the colors of the 1) base and four walls of the fish tank 2) above and 3) below
the water level when viewed from the top.
The reason to have two quite similar situations in the LRRT is that the first situation
would give students opportunity to apply the concepts of reflection, refraction and total internal
reflection while the second situation is given to check the consistency of students’ reasoning in
answering the questions in the first situation. One of the criticisms of multiple-choice items is
that students giving correct answers do not necessarily mean they have mastered the content
(22). In other words, it is possible to answer correctly for many reasons, including guessing. To
double check this criticism, two or more items having the same concept application but in
different situation has been developed. This helps the educator/teacher to verify whether the
particular student have really understood the given concept and have not given the correct
answer by guessing.
Results
The students’ responses to the LRRT are analyzed in 4 parts. The first part is about the
difficulty index and item discrimination index of each item. The inconsistency found in students’
response while answering the questions that required the application of the same concept have
been analyzed in the second part. The third part presents the students’ misconceptions on the
relevant optics concepts. Analysis of students’ responses who used their real life experience
instead of optics concepts is presented in the last part.
Difficulty index and discrimination index
Table 1 presents the difficulty index and item discrimination index of each item. The
difficulty indexes for the items range from 0.23 to 0.69. For items 1e, 2b and 2c, having low
difficulty indexes might be because students had difficulty to visualize the situations in their
mind. Especially, item 2c requires two concepts; light refraction and reflection. These items need
to be revised for further studies. However, a good item can sometimes be answered incorrectly
by a majority of students because it addresses a particularly deep-rooted misconception or
reasoning difficulty that is not easily reversed by instruction (21). The values of all point-biserial
discrimination indexes for all items are positive and greater than 0.30 which indicates that the
items serve well to discriminate between students with higher and lower levels of knowledge
(21).
Table 1: Item difficulty and discrimination index of each item in the LRRT
Students’ inconsistency in application of same concepts
TablesItems
2 and 3 categorize the
items1bin accordance
to1dthe concepts
application
required
to
1a
1c
1e
2a
2b
2c
Difficulty index
Item Discrimination index
0.69
0.52
0.32
0.38
0.43
0.37
0.39
0.36
0.24
0.37
0.51
0.52
0.23
0.42
0.25
0.50
Students’ inconsistency in application of same concepts
Tables 2 and 3 categorize the items in accordance to the concepts application required to
answer the items. These tables show the number of students who gave the correct answers in first
and second situations respectively. To be able to reason out what happens in both the situations,
students should understand the basic concepts of optics as follows:


The reason for seeing any opaque object is that the light rays fall on it and gets reflected
into the eyes.
When a light ray propagates from air to glass, it gets bent and passes through.

When a light ray propagates from water to air at more than the critical angle, it gets
totally reflected back in water. This phenomenon is called “total internal reflection”.
However, the results shown in Tables 2 and 3 clearly indicate that students had poor
ability to apply relevant concepts of optics in the fish tank situations. The overall score in the
test was only 38.3%.
Table 2: Result of items in the first situation
Concept
Light reflection
Total internal reflection
Light refraction
Light reflection
Total internal reflection
Item
1a
1b
1c
1d
1e
No. of correct answers (students)
76
36
48
43
27
No. of correct answers (%)
68.5
32.4
43.2
38.7
24.3
Table 3: Result of items in the second situation
Concept
Item
Light reflection
Total internal reflection
Light refraction and
reflection
2a
2b
No. of correct answers
(students)
56
26
2c
28
No. of correct answers (%)
50.5
23.4
25.2
When the answers of questions in both situations based on same concept were compared,
a lot of inconsistency was found. In item 1a, students were asked to give the color of the base of
the half-filled transparent tank when viewed from the top; 68.5% of the students gave the correct
answer. However, in item 2a where students were asked to give the color of the base of the halffilled tank (wrapped with yellow paper on three side wall as shown in figure 2) when viewed
from the top, their score dropped to 50.5%. Similarly item 1d asked students to give the color of
the base for completely filled tank which required the same concept as the other two items 1a
and 2a; yet the score for this item greatly changed to 38.7%. Only 21 students could give correct
answers for all the three questions.
The concept required for answering items 1b, 1e and 2b was total internal reflection of
light. Students were asked to give the color of the walls below the water level of the tank. The
phenomenon can be explained as follows: the rays of light travelling from air to water fall on the
base of the container and are reflected back. Some of these reflected light rays fall on the walls
below the water level at angle greater than the critical angle, they are then totally reflected
giving the color of the walls same as the color of the base. Only 32.4% of the students gave the
correct answer for 1b and the result further decreased to 24.3% and 23.4% when they answered
for item 1e and 2b respectively. Only 4 students gave the correct answers for all these three
questions.
Students’ misconceptions
The students’ misconceptions can be categorized as follows: 1) misunderstanding about
propagation of light; 2) misunderstanding in determining the color of an object. Tables 4 and 5
present the percentage of students having the categorized misconceptions in each item.
Table 4: Misunderstanding about propagation of light
Misconception about propagation of light
1. Light rays are totally reflected when they travel
from air (less dense) to water (more dense).
2. The objects are seen by our eyes only if they lie
straight in front of our eyes.
Percentage of students showing the misconception in
each item
Questions for
Questions for First Situation
Second Situation
1a
1b
1c
1d
1e
2a
2b
2c
16.2
23.4
18.9
-
-
14.4
12.6
11.7
-
19.8
6.3
-
12.6
-
7.2
7.2
Table
5: Result
Misunderstanding
in determining
the color of an object
Table 3:
of items in the
second situation
Percentage
No. of correct
answersof students showing the misconception
Conceptin determiningItem
correct answers (%)
in No.
eachofitem
Misconception
the color of an (students)
object
Questions for
Light reflection
2a
56
50.5
Questions for First Situation
Second
Situation
Total internal reflection
2b
26
23.4
1a
1b
1c
1d
1e
2a
2b
2c
Light refraction and
2cthe quantity of
28
25.2
3. Water color
changes
to
blue
when
reflection
27.0 20.7
water increases.
4. An opaque object becomes colorless when placed
14.4
14.4
6.3 10.8 21.6
over a transparent colorless object.
5. If two different colored papers are observed
14.4 21.6 19.8
through water, we see the mixed color.
For the first misconception, some students believed that the surface of the water in the
fish tank appear to be silver when viewed from top. They believed that total internal reflection
occur at the surface of water when light rays travel from air to water. Some of the students had
the idea that they would not be able to see the side walls when viewed from the top as light rays
travel in straight line. This response revealed the second misconception. For the third
misconception, some students thought that the density of water increases with the increase in
quantity of water and thus looks blue in color. The fourth misconception was found when the
students were asked the color of the base. Some of them had the notion that the colored base
would become colorless when it was seen through colorless and transparent glass and water. For
the fifth misconception, students were asked about the color of the base and walls when viewed
from the top. They used the color mixing concept as they chose the option which stated “Green
because of mixture of blue color and yellow color”.
Effect of real life experience
Table 6 presents the percentage of students who used their daily life experience to answer
some questions. 0.9%, 19.8% and 1.8% of the students did not at all apply the concepts of light
reflection to answer item 1a, 1d, and 2a as they opted for the option, “Not visible because the fish
tank is deep”. Since rivers in Bhutan look blue in color, some students related this experience to
answer items 1d and 1e, for which the water level is increased from half-filled to completely
filled tank. Students believed that water color changes to blue because its quantity is increased.
These are the clear examples of application of non-scientific real world explanation.
Table 6: Percentage of students applying daily life experience to answer the questions
Explanation related to daily life experience
1. The base is invisible because the fish tank is deep.
2. Water color changes to blue when the quantity of
water increases.
Percentage of students who did not apply the
optics concepts
Second
First Situation
Situation
1a
1b
1c
1d
1e
2a
2b
2c
0.9
19.8
1.8
-
-
-
27.0
20.7
-
-
-
Discussion and Conclusion
Our study clearly indicates that the Bhutanese students have poor ability to apply the
optics concepts to explain the situations related to a fish tank even after the formal teaching of
these concepts. In addition, students occasionally use their real life experiences which contradict
with the scientific explanation to answer the questions. Choosing options like “the base is
invisible because the fish tank is deep” and “the base is blue because water color becomes blue
when quantity of water increases” precisely proves this finding.
We suspect that the students memorize the concepts, laws, formulas and the ray diagrams
and wrongly apply in these situations. For instance, students had learnt the concepts of total
internal reflection of light but while applying in the fish tank situations some of them applied it
in a wrong way as we discussed in the previous section. They thought that light rays travel from
air to water and get totally reflected. Also, students learnt about color mixing concept yet they
had applied this concept in a wrong way in the second situation. Furthermore, prominent
inconsistency in answering items having same concepts also indicates that students lack
scientific problem solving skill. This skill is defined as the ability and the consistency to use a
concept to solve a set of problems (23).
Hence it is very important for the teachers to explain these concepts to students
experimentally and also let students do some hands-on-activities wherein students can
understand the direction of propagation of light from object to eye. Teachers should also make
effort to let students draw ray diagrams for situations that are not mentioned in the textbooks to
check whether they have really understood the concepts and have gained ability to apply the
concepts in variety of situations.
This study showed that students’ prior knowledge and misconceptions need to be
carefully considered while teaching the relevant optics concepts. It also implies an urgent need to
work for improvement of assessment process by developing similar tests in other topics of
physics. It is hoped that this study will assist teachers to better understand their students’
misconceptions and that our results will guide teachers to a more effective student-centered
teaching approach and the development of learning activities that improve students’
understanding.
Although the results gave significant information about the students’ conceptions in
properties of light, we cannot statistically generalize to a larger universe. Since only a single data
source was used, it could be a limitation to this study. Therefore, for further work, clinical
interviews to probe for detailed information about students’ conception of light would be very
helpful. The information gathered could be used in developing better and relevant teaching
materials, strategies and approaches to teach the fundamental concepts in light.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Blizak D, Chafiqi F, Kendil D, editors. Students Misconceptions about Light in Algeria 2009: Optical Society
of America.
Langley D, Ronen M, Eylon BS. Light propagation and visual patterns: pre instruction learners’ conceptions
J.Re.Sci.Teach. 1997 34 399–424
Pompea SM, Dokter EF, Walker CE, Sparks RT, editors. Using Misconceptions Research in the Design of
Optics Instructional Materials and Teacher Professional Development Programs 2007: Optical Society of
America.
Anderson CW, Smith EL. Children's Conceptions of Light and Color: Understanding the Role of Unseen Rays.
ERIC database. 1986: (ED408570).
Fetherstonhaugh A. Misconceptions and light: A curriculum approach. Research in Science Education. 1990
20(1):105.
Fetherstonhaugh T, Treagust DF. Students’ understanding of light and its properties: teaching to engender
conceptual change Sci. Ed. 1992: 76 653–72
Galili I, Bendall S, Goldberg F. The Effects of Prior Knowledge and Instruction on Understanding Image
Formation. Journal of Research in Science Teaching. 1993; 30(2):271-301. PubMed PMID: 21527967.
Goldberg FM and McDermott LC. Student difficulties in understanding image formation by a plane mirror.
Phys. Teach. 1986: 24 472–80
Andersson, B, Karrqvist, C. How Swedish pupils, age 12-15 years, understand light and its properties. European
Journal of Science Education, 1983 5(4), 387-402.
Hubber P. Secondary students' perceptions of a constructivist-informed teaching and learning environment for
geometric optics. Teaching Science: The Journal of the Australian Science Teachers Association. 2005;
51(1):26-9. PubMed PMID: 18139786.
Sethi RC. ICSE Innovative Physics for Class IX. 2012 ed. Delhi: Good Luck Publishers Ltd.
Sethi RC. ICSE Innovative Physics for Class X 2012 ed. Delhi: Good Luck Publishers Ltd.
Johnson D, Childs A, Ramachandran K, Tenzin W. A needs assessment of science education in Bhutan. Paro:
Ministry of Education; 2008. 30 p.
Haladyna TM, Downing SM, Rodriguez MC. A review of multiple-choice item-writing guidelines for
classroom assessment. Applied measurement in education. 2002; 15(3):309-33.
Kahle EC, Scherr RE, Close HG. An Evolving Model for Seeing Colored Objects: A Case Study Progression.
AIP Conference Proceedings. 2010; 1289(1):185-8.
16. Yalcin M, Altun S, Turgut U, Aggül F. First Year Turkish Science Undergraduates’ Understandings and
Misconceptions of Light. Sci Educ. 2009 2009/08/01; 18(8):1083-93.
17. Gregg V, Winer G, Cottrell J, Hedman K, Fournier J. The persistence of a misconception about vision after
educational interventions. Psychonomic Bulletin & Review. 2001 2001/09/01; 8(3):622-6.
18. Masters MF, Grove TT. Active learning in intermediate optics through concept building laboratories. American
Journal of Physics. 2010; 78:485.
19. Breslow R. Optics in a fish tank. The Physics Teacher. April, 1976; 14(4):234.
20. DCRD. The syllabus for class nine and ten. Thimphu, Bhutan: Department of Curriculum Research and
Development. 2013.
21. Bardar EM, Prather EE, Brecher K, Slater TF. Development and Validation of the Light and Spectroscopy
Concept Inventory. Astronomy Education Review. 2006 09/00/; 5(2):103-13.
22. Dufresne RJ, Leonard WJ, Gerace WJ. Making sense of students' answers to multiple-choice questions. The
Physics Teacher. 2002; 40: 174.
23. Nopparatjamjomras S. A new approach to teach colored light and color perception for high school students by
using colored light mixer. Thailand: Mahidol University; 2008.