An 107-mm-focal-length lens is used to focus an image on the sensor of a camera.

Question

An 107-mm-focal-length lens is used to focus an image on the sensor of a camera. The maximum distance allowed between the lens and the sensor plane is 134 mm . How far in front of the sensor should the lens (assumed thin) be if the object to be photographed is 10.0 m away from the lens? Follow the sign conventions. How far in front of the sensor should the lens (assumed thin) be if the object to be photographed is 3.0 m away from the lens? Follow the sign conventions. How far in front of the sensor should the lens (assumed thin) be if the object to be photographed is 1.0 m away from the lens? Follow the sign conventions. What is the closest object this lens could photograph sharply? Follow the sign conventions.

Explanation / Answer

f = 107 mm = 10.7 cm = 0.107 m

q_max = 134 mm = 0.134 m

1. object distance, p = 10 m

1/f = 1/p + 1/q

1/0.107 = 1/10 + 1/q

q = 0.108 m Or 108 mm .....Ans

2. p = 3 m

1/0.107 = 1/3 + 1/q

q = 0.111 m Or 111 mm .....Ans

3. 1/0.107 = 1/1 + 1/q

q = 0.120 m Or 120 mm .....Ans

4. q = 0.134 m

1/0.107 = 1/p + 1/0.134

p = 0.531 m Or 53.1 cm ....Ans

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