Chapter 15.2

Bending of Light
• Any transparent object that is curved with affect the path of light rays.
• Ex: o Glass bottle full of water will affect the image of an object.
o Your eye’s muscles expand and contract causing the lens in your eye to change shape and therefore allow people to focus on different objects.

Lens
• Lens – A transparent object that refracts light rays, causing them to converge or diverge to create an image.

Converging Lens
• Converging Lens – A lens where the middle part of the lens is thicker than the rim.
• Also known as a convex lens.

Diverging Lens
• Diverging Lens – A lens where the middle part of the lens is thinner in the middle and thicker around the rim.
• Also known as a concave lens.

Focal Length
• Each lens has two focal points (F), therefore there are two focal length (f).
• A focal length is measured from the focal point to the center of the lens (normal).
• The focal points lay on the principal axis.

Converging & Diverging
Focal Points
• For converging lens, the focal point is located at the point where the rays of light meet at a single point.
• For diverging lens, the focal point is located at a point from which the diverged rays appear to originate.

Rules For Drawing Ray
Diagrams of Converging Lens
Ray
Parallel Ray
Central Ray
Focal Ray
From object to lens From lens to image
Parallel to Principal Axis Passes through focal
Point
To the center of lens
(Where normal meets principal axis)
Straight through from the center of the lens
Passes through front focal point
Parallel to principal axis

Ray Diagrams for
Converging Lens

Ray Diagrams for
Converging Lens

Ray Diagrams for
Converging Lens

Rules For Drawing Ray
Diagrams of Diverging Lens
Ray
Parallel Ray
Central Ray
Focal Ray
From object to lens From lens to image
Parallel to Principal Axis Directed away from front focal point
To the center of lens
(Where normal meets principal axis)
Straight through from the center of the lens
Proceeding towards back focal point
Parallel to principal axis

Ray Diagrams for
Diverging Lens

Characteristics of
Converging Lens
• Image is always real, unless object is in front of the focal point.
• Image is always on the opposite side the lens, unless the object is in front of the focal point.
• Image is always inverted, unless object is in front of the focal point.

Characteristics of
Diverging Lens
• Image is always virtual (Imaginary).
• Magnification is less than 1.
• Image is always upright.
• Image is formed on the same side as the object.

Thin-Lens Equation
1
+ 𝑝
1 𝑞
=
1 𝑓 p = Object Distance
- Always Positive q = Image Distance
- Negative ( Object side of lens)
- Positive (Opposite side of Lens) f = Focal Length
- Positive (Converging Lens)
- Negative (Diverging Lens)

Magnification Equation ℎ ′
𝑀 = = − 𝑞 ℎ 𝑝
M = Magnification
- Positive (Upright Image)
- Negative (Inverted Image)
- M>1 (larger Image) M<1 (Smaller Image) h = Object Height h‘ = Image Height p = Object Distance q = Image Distance

Example Problem
• An object is placed 30.0cm in front of a converging lens that has a focal length of 10.0cm. Find the image distance and magnification.

Example Problem Answer
1
+ 𝑝
1
30.0𝑐𝑚
+
1 𝑞
1 𝑞
=
= 𝒒 = 𝟏𝟓𝒄𝒎
1 𝑓
1
10.0𝑐𝑚
𝑀 = ℎ ′ ℎ
𝑀 = − 𝑞
= − 𝑞 𝑝
15𝑐𝑚
= 𝑝 30.0𝑐𝑚
𝑴 = −𝟎. 𝟓𝟎