Ph272- General Physics II (Electricity and Magnetsism)

Lecture 28: Ch. 34 - Thin Lenses, Chromatic Aberration

Key Topics

Overview

• In principle, all you need to know is the Law of Refraction to determine the image produce by a lens.
• In practice, for thin lenses all you need to locate the two focal points of the lens.
• Again, you will learn two ways to construct the image:(1) ray tracing (geometric method) and (2) algebraic method. The algebraic method uses exactly the same equation as for spherical mirrors except there is a change in convention (s' =negative still mean a virtual image but located on the same side of the lens as the object. The ray tracing is similar but not exactly the same as that mirrors.

Converging lens

• Image construction:

Unlike mirrors, a lens has two focal points, one on each side of the lens.

(1) Ray tracing: Same method as for spherical mirrors, you can pick any two rays from the same point on the object. Again, there are two particular rays that are most convenient:

One is the horizontal ray (i.e. parallel to the axis), it is refracted to the focal point on the outgoing side of the lens.

One is a ray passing througth the focal point on the incoming side, it is refracted horizontally on the outgoing side it is unrefracted.

(To check the the accuracy of your ray tracing, you can draw one more ray, a ray passing throught the center of a thin lens is unrefracted, i.e. no bending. This third refracted ray should intersect at the same point as the previous two rays.).

At what object distances will you get a virtual image and at what object distances will you get a real image?

Again consider 3 regions:

Region (1) : object distance (s) < f, region (2): f < s < 2f and region (3): 2f < s

Construct the images for these three situation and characterize the image by stating the location of image (which region), virtual or real; enlarged or reduced; upright or inverted.

(2) Algebraic method: 1/s + 1/s' = 1/f ; f = positive (Eq. 31-6, P. 101)

This is the same equation as for the concave shperical mirror, so the results are exactly the same excepted that when s' = negative (a virtual image), it is on the

For a single thin lens, s is always positive because either side of a lens can be th eincoming side. For virtual images s' =negative, therefore m = positive => virtual images are upright. For real images, s' = positive and m =negative => real images are inverted (same conclusion as for a single mirror).

• Flat lens limit: If the radius focal length approaches infinity then a curved lens approaches a flat lens.

Eq. 31-6 => 1/s + 1/s' =0. Does this equation describe a flat lens? (Calculate s' and m)

Diverging Lens

• Image construction:

(1) Ray tracing: Same method as for converging lens.

Consider 3 regions:

Region (1) : object distance (s) < |f|, region (2): |f| < s < |2f|, and region (3): |2f| < s

Construct the images for these three situation and characterize the image by stating the location of image (which region), virtual or real; enlarge or reduced; upright or inverted. You will find that all 3 regions behave the same for a diverging lens (just like a convex mirror).

(2) Algebraic method: 1/s + 1/s' = 1/f ; f = negative (Eq. 31-6, P. 101)

Calculate s' for s in the three region and compare with the ray tracing results (pick some numbers for s and f and calculate s')

Manipulate Eq. 30-6 to find s' and m (m=-s'/s) and therefore show that:

For a single diverging lens, all images are virtual, inverted, and reduced (same as for convex mirror).

Chromatic aberration.

• There is aberration (like spherical aberration) due to the shape of the lens.
• In addition to that, there is an aberration due to the index of refaction is different for different frequencies hence different focal point for different color of light.
• => a white light (consists of many colors) will not focus into a single spot, a fussy color spot appears, this is called chromatic abberation.

Review

• Write a brief review here

Go to top of page

Ph272 homepage