A lighted candle is placed 36 cm in front of a diverging lens. The light passes

Question

A lighted candle is placed 36 cm in front of a diverging lens. The light passes through the diverging lens and on to a converging lens of focal length 10 cm that is 5 cm from the diverging lens. The final image is real, inverted, and 18 cm beyond the converging lens. Find the focal length of the diverging lens.
cm

A coin is located 18.0 cm to the left of a converging lens (f = 14.0 cm). A second, identical lens is placed to the right of the first lens, such that the image formed by the combination has the same orientation as the original coin but 1.4 times its size. Find the separation between the lenses.

Explanation / Answer

here,

image distance for converging lens, di = 18 cm

focal length of converging lens , fd = 10 cm

let the object distance for converging lens be do

using lens formula

1/f = 1/di + 1/do

1/10 = 1/18 + 1/do

do = 22.5 cm

for diverging lens

image distance , i =- 22.5 + 5

i = - 17.5

object distance , o = 36 cm

let the focal length be fc

using lens formula

1/fc = 1/i + 1/o

1/fc = - 1/17.5 + 1/36

fc = - 34.05 cm

the focal length of the diverging lens is - 34.05 cm

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