Chapter 24 & 25

Geometrical Optics &
Physical Optics

Spherical Thin Lenses

Thin-Lens Equation
Lensmaker's Formula

(1)

Geometry of the Thin-Lens Equation

Example 1

The lens shown in the diagram below is generally used in air. If it is placed in water instead, does its focal length (a) increase, (b) decrease, or (c) stay the same?

Solution:

The focal length increases.

Focal Points

(2)

Example 2

A double convex lens is to be made of glass with an index of refraction of 1.5. One surface is to have twice the radius of curvature of the other and the focal length is to be 60 mm. What are the radii?

Solution:

Use the lens maker's equation:

Then use the substitution in the above equation and solve for :

Therefore, the radii are 45 mm and 90 mm.

Thin Lens Equation
Gaussian Lens Equation

(3)

Sign Convention for Spherical Refracting Surfaces and Thin Lenses
	+ left of O
	+ right of O
R	+ if C is right of O
	+ above optical axis

Magnification

(4)

(5)

Meanings Associated with the Signs of Various Thin Lens Parameters
	Sign
Quantity	+	–
	Real Object	Virtual Object
	Real Image	Virtual Image
f	Converging Lens	Diverging Lens
	Erect Object	Inverted Object
	Erect Image	Inverted Image
	Erect Image	Inverted Image

Example 3

A lens produces a real image that is twice as large as the object and is located 15 cm from the lens. Find the focal length of the lens and the object distance.

Solution:

Use the magnification equation to find the object distance:

Use the thin-lens equation to find the focal length:

f = 5.0 cm

Example 4

An object is placed 12 cm in front of a diverging lens with a focal length of -7.9 cm. Find (a) the image distance and (b) the magnification.

Solution:

Use the thin-lens equation to find the image distance:

Use the magnification equation to find the magnification:

Example 5

A flint glass prism is made in the shape of a 30°-60°-90° triangle, as shown in the figure. Red and violet light are incident on the prism at right angles to its vertical side. Given that the index of refraction of flint glass is 1.66 for red light and 1.70 for violet light, find the angle each ray makes with the horizontal when it emerges from the prism.

Solution:

Use Snell's Law for the red light:

Do the same thing for the violet light:

On to Lenses Part 3