a. An object 5 cm high (an arrow say), is placed at x = 0 cm. A thin lens of foc

Question

a. An object 5 cm high (an arrow say), is placed at x = 0 cm. A thin lens of focal length +20 cm is placed at x = 50 cm. Another thin lens of focal length + 5 cm is placed at 85.0 cm. If you look through both lenses at the object, where will you see the image, and what will be its magnification (lateral magnification)?

b. You reach into a pool of water (n=1.33) to retrieve a coin on the bottom. The coin looks to be 30 cm deep, so you roll up your sleeve that much to avoid getting it wet. Focusing on the coin as your reach for it, you fail to notice until too late that your rolled-up shirt-sleeve is completely immersed. About how deep was the coin really?

Explanation / Answer

Part A)

For the first lens

1/f = 1/p + 1/q

1/20 = 1/50 + 1/q

q = 33.3 cm

For the second lens

1/5 = 1/1.67 + 1/q

q = -2.5

The image will be located at 82.5 cm

The magnification is -33.3/50 times 2.5/1.67

M = .997 (pretty close to 1)

Part B)
Apply q/p = -n2/n1

-30/p = -1/1.33

p = 39.9 cm

The actual depth was 39.9 cm

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