Changing the f-number of a camera lens by 4X will change the light intensity adm

Question

Changing the f-number of a camera lens by 4X will change the light intensity admitted to the film by what factor? A) 16 B) 2 C) 025 D) 0.0625 E) 4 Two convex thin lenses with focal lengths 8 and 14 cm, respectively, are aligned on a common axis, running left to right the 8 cm lens being on the left. The lenses are separated by a distance of 20 cm. An object is located at a distance of 26 cm to the left of the 8 cm lens. Where will the final image appear as measured from the 14 cm lens? A) -21.28 cm B) 9.296 cm C) -431 cm D) 11,024 cm E) 17.333333 cm

Explanation / Answer

14. since the intensity of the light would depend on the area of the aperture, when aperture is increased by 4x, the diameter of the aperture is increased by 4 times

hence, the area becomes 16 times the original area

hence the intensity admitted should also increase by 16 times

so the answer would be

A) 16

15. given

focal length of left lens, fl = 8 cm ( +ve because it is a convex lens)

focal length of right lens, fr = 14 cm

distance seperating the lenses, d = 20 cm

object distance for left lens, u = -26 cm

let the image distance for this lens be v

then from lens formula

1/v - 1/u = 1/fl

1/v = 1/8 - 1/26

v = 11.55 cm to the right of first lens

hence, object distance for second lens, u' = -(20 - 11.55) = -8.444 cm

let image ditance be v'

then

1/v' - 1/u' = 1/fr

1/v' = 1/14 - 1/8.444

v' = -21.28 cm

so the answer is A) -21.28 cm

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