MIRRORS
Purpose: To study the formation of images by different types of mirrors.
Apparatus: Plane mirror with holder, pair of compasses, concave-convex cylindrical
mirror, scale, protractor, pins, pin board.
References:
Discussion:
The image formed by a plane mirror or by a convex mirror, of an object placed in
front of it will always be virtual, and may be located by tracing the rays which appear
to come from the image behind the mirror. Hence, the virtual image may be located by
sighting at the image from two different directions and projecting these two lines of sight
backwards until they intersect (behind the mirror). The same will be true of an object
placed in front of a concave mirror if the object is at a distance from the mirror less than
its focal length. The image of an object in front of a concave mirror will be real if the
object is at a distance from the mirror greater than its focal length. In this case the
method used in locating the image is the same as above, but the two lines of sight will
intersect in front of the mirror, thereby indicating a real image.
In this exercise, and all through your work in optics, represent the actual path of
all rays of light by solid lines; and represent virtual rays ( prolongations of actual ray
paths ) by light broken lines. Optical surfaces should be represented by heavy solid lines.
All diagrams are original data and must be included in the report.
Top view of image location for a plane mirror is shown in Fig 9-1.
Procedure:
1. Draw a straight line across the center of a sheet of paper; this is the "mirror
line". Set up the plane mirror in its holder on the mirror line so that the actual mirror
surface, the front surface, is on the line. (Refer to Fig. 9-1). Set the hat pin up 10 cm in
front of the mirror line and make sure it is vertical. This is the object O and its
(perpendicular ) distance from the mirror is the object distance, p. Place a pin (L Pin #1)
about 5 cm in front of the mirror and a few centimeters to one side of the normal. Bend
down to the level of the paper and, while looking at this pin, move your head about until
the image of O is directly behind L pin #1. Place a second pin (L Pin #2) about 10 cm
from the first one so that the two sighting pins and the image of the hat pin are in one
straight line. If all the pins are standing vertically the second pin will hide the first one as
well as the image of O. The image will then lie somewhere along the line joining the
points of the two sighting pins.
Repeat this procedure by placing a pin about 5 cm in front of the mirror and a few
centimeters to the other side of the normal. ( R Pin #1)
Remove the mirror from the paper and carefully extend the two " lines of sight "
backwards until they intersect at the image I. Draw a straight line connecting O and I.
Measure the angle between the mirror line and the line O-I. The precision of the results of
this measurement depends upon the sharpness of your pencil and the care with which you
taken in sighting and drawing the lines. What should this angle be ? If your result is more
than 10 degrees from the expected value, repeat the procedure.
2. On a new sheet, draw a line O-O' , 5 cm long at an angle of about 45 degrees
with respect to the mirror line and which, if extended, will intersect the mirror line on the
paper. Locate I and I', the images of O and O' as in part 1.
Measure the length of the line I-I'. Compare to the length of O-O'.
Measure the angle between O-O' and the mirror line.
Measure the angle between I-I' and the mirror line. Compare the two angles.
3. On another sheet draw the curved mirror line of the concave cylindrical mirror
(not the convex side ) near the top of the paper. Locate its center of curvature by erecting
the perpendicular bisectors on any two chords and locating their point of intersection.
Check this point by moving the hat pin along the principal axis until the image of the pin
coincides, without parallax, with the pin itself. Locate the principal axis and the pole or
vertex of the mirror. Measure the radius of curvature (r) of the mirror and mark on the
paper the point halfway between the pole or vertex and the center of curvature. The point
so marked is the principal focus, F.
At a point on the axis 16 cm from the pole draw a line 1.5 cm long perpendicular
to the axis of the mirror starting from the axis. Mark the end points of this line O and O',
and put an arrowhead at the outer end of the line, O. This line will represent the object;
the object distance, p, is thus 16 cm; the object size, S, is 1.5 cm. Set up the hat pin at the
point O for sighting. Locate the image of the tip by sighting from two directions, as in
procedure (1). Where must the image of the point O of object be ? Repeat for the O'.
Measure the size of the image, S', and the image distance q. Mark the image line II' and
mark an arrowhead on the image.
4. Again draw the curved mirror line near the top of another sheet of paper and
locate the center of curvature. As before, construct an object 1.5 cm long at a distance of
16 cm from the mirror. Locate the image this time by the method of image construction,
not by actual sighting. Measure S' and q.
5. On another sheet, near the center, draw the mirror line of the convex cylindrical
mirror. Locate its center of curvature by construction. Indicate the focus. Determine by
both methods, sighting and ray construction, the image size and distance in the case of
the convex mirror, again making S = 1.5 cm and p = 16 cm. Two separate diagrams will
be needed.
6. In this part, merely notice the changes in the image as an object is moved away
from the surface of the spherical concave or convex mirrors. These qualitative
observations should be recorded in your discussion.
Calculations:
Calculate the ratio q/p for all objects and their corresponding images in parts (1),
(2), (3), (4) and (5). Also calculate the ratio S'/S in parts (2), (3), (4) and (5) and compare
these with the corresponding ratios of q/p.
Calculate for all images formed by curved mirrors the focal length f from the
relation 1/p + 1/q = 1/f.
In your tabular summary indicate the kind of mirror used and by what method
each image was found. Tabulate p, q, S, S', q/p, S'/S, r/2, f(calculated) and the type of
image.
Designate the type of image formed as : real or virtual; erect or inverted; enlarged
or diminished.
Questions to be Answered in the Report
1.What is meant by a virtual image? Under what conditions will a concave mirror
give a virtual image?
2. In part (3) you observe the real image of a pin. Why did the pin not appear
inverted?
3. What kind of mirror does a dentist use when he wants to observe a magnified
image of a tooth, and where does he locate it for this purpose?
4. In a projection lantern at least half the light from the lamp is headed in the
wrong direction; where would you put a mirror and what type would you use, to return
this light to the vicinity of the filament, this time headed in the right direction?
5. As one approaches a concave mirror from a large distance, his image may
vanish from his sight. For this effect to be most complete, where should the image be: at
infinity? at the mirror's principal focus? on his eyeball? At that moment, where should the
observer be?