1. The focal length of an f/4 camera lens is 300 mm . Part A: What is the apertu

Question

1. The focal length of an f/4 camera lens is 300 mm .

Part A: What is the aperture diameter of the lens?

Part B: If the correct exposure of a certain scene is 1/250s at f/4, what is the correct exposure at f/22.6?

2. Your digital camera has a lens with a 54 mm focal length and a sensor array that measures 4.82 mm× 3.64 mm. Suppose you’re at the zoo, and want to take a picture of a 4.55 m tall giraffe.

Part A: If you want the giraffe to exactly fit the longer dimension of your sensor array, how far away from the animal will you have to stand? Express your answer with the appropriate units.

3. Contact lenses are placed right on the eyeball, so the distance from the eye to an object (or image) is the same as the distance from the lens to that object (or image). A certain person can see distant objects well, but his near point is 44.0 cm from his eyes instead of the usual 25.0 cm .

Part A: If the correcting lenses will be contact lenses, what focal length lens is needed ?

Part B: What is the power corresponding to the focal length found in part (C) in diopters?

4. A person can see clearly up close, but cannot focus on objects beyond 72.0 cm . She opts for contact lenses to correct her vision.

Part A: What focal-length contact lens is needed ?

Part B: What is the power of the contact lens in diopters?

5. A simple magnifier for viewing postage stamps and other pieces of paper consists of a thin lens mounted on a stand. When this device is placed on a stamp, the stand holds the lens at the proper distance from the stamp for viewing.

Part A: If the lens has a focal length of 11.8 cm , and the image is to be at infinity, what is the angular magnification of the device ?

Part B: If the lens has a focal length of 11.8 cm , and the image is to be at infinity, how high should the stand hold the lens above the stamp?

Explanation / Answer

3)

a)

f = 1/s' + 1 / s

f = ss' / (s + s')

here s = 25 cm and s' = - 44 cm

f = 25*-44 / (25 - 44) = 57.90 cm

b)

Diopters is the inverse of f in meters = 1/f = 1 / 0.5790 = 1.727 diop.

4)

a)

1/f = 1/s + 1/s'

s tends to the infinity

:- f = - 72 cm = - 0.72 m

negative sign because lens is diverging.

b)

P = 1 / f = 1 / -0.72 m = 1.39 diop.

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