A zoom lens is a lens that varies in focal length. The zoom lens on a certain di

Question

A zoom lens is a lens that varies in focal length. The zoom lens on a certain digital camera varies in focal length from 6.50 mm to 20.1 mm . This camera is focused on an object 2.30 m tall that is 1.35 m from the camera.

Part A: Find the distance s1 between the lens and the photo sensors and the height h1 of the image when the zoom is set to 6.50 mm focal length. Enter your answers separated by a comma. (unit in mm)

Part B: Find the distance s2 between the lens and the photo sensors and the height h2 of the image when the zoom is set to 20.1 mm. Enter your answers separated by a comma. (unit in mm)

Part C: Which is the telephoto focal length, 6.50 mm or 20.1 mm ?

Explanation / Answer

(A) f1 = 6.50 mm = 0.65 cm

Object distance, p1 = 135 cm

Applying, 1/f1 = 1/p1 + 1/q1

1/0.65 = 1/135 + 1/q1

q1 = 0.653 cm Or 6.53 mm ..........Ans

m = - q1 / p1 = hi / ho

- 0.653 / 135 = hi / 2.30

hi = 0.0111 m Or 11.1 mm .......Ans

(B) f= 20.1 mm = 2.01 cm

1/2.01 = 1/135 + 1/s2

s2 = 2.04 cm Or 20.4 mm . ........Ans

h2 = (2.04 / 135) (2.30) = 0.0348 m Or 34.8 mm .......Ans

(C) 20.1 mm

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