## Mastering Physics Solutions: A Two-Lens System

A Two-Lens System

Part A = 31.8 cm
Part B = 0.236 cm
Part C = Upright
Part D = 19.42 cm
Part E = The image is a different size and oriented differently.

Solution Below:

A compound lens system consists of two converging lenses, one at x = -20.0 cm with focal length f1 = +10.0 cm, and the other at x = +20.0 cm with focal length f2 = +8.0 cm . An object 1.00 centimeter tall is placed at x = -50.0 cm.

Part A

What is the location of the final image produced by the compound lens system? Give the x coordinate of the image.
Express your answer in centimeters, to three significant figures or as a fraction.

Start by finding V2:

v2 = 1/(1/f2 – 1/u2)
v2 = 11.8 cm

Add v2 to the position of the second lens gives x = 31.8 cm

31.8 cm

Part B

How tall is the image?
Express your answer in centimeters, to three significant figures or as a fraction.

Use the formula v1 * v2 /(u1 u2)

This gives a height of 0.235 cm

Note: MasteringPhysics wants an answer of 0.236 cm

0.236 cm

Part C

Is the final image upright or inverted, relative to the original object at x = -20 cm?

Upright

Part D

Now remove the two lenses at x = +20 cm and x = -20 cm and and replace them with a single lens of focal length fs at x = 0. We want to choose this new lens so that it produces an image
at the same location as before.
What is the focal length of the new lens at the origin?
Express your answer in centimeters, to three significant figures or as a fraction.

The object is 50 cm from the new lens and has an image distance of 31.76 cm. This gives an answer of 19.42 cm.

19.42 cm

Part E

Is the image formed by fs the same size as the image formed by the compound lens system? Does it have the same orientation?

The object is 50 cm from the new lens and has an image distance of 31.76 cm. This gives an answer of 19.42 cm.

The image is a different size and oriented differently.

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### 4 Responses to Mastering Physics Solutions: A Two-Lens System

1. Eric says:

The answer to B is 4/17 cm = 0.235 cm and not 400/17 cm = 23.5 cm. However, the part about mastering physics wanting 0.236 cm is true, but the fraction seems to work just fine.

• Mastering Physics Solutions says:

Yes indeed- thanks for the catch. If the fraction works, that’s great!

2. Mårten says:

At part B the answer is 0.236 cm, not 23.6

• Mastering Physics Solutions says:

Good catch, sorry for the confusion!