As shown in the figure a candle is at the center of curvature of a concave mirro

Question

As shown in the figure a candle is at the center of curvature of a concave mirror whose focal length is 13.0 cm. The converging lens has a focal length of 30.5 cm and is 85.0 cm to the right of the candle. The candle is viewed through the lens from the right. The lens forms two images of the candle. The first is formed by light passing directly through the lens. The second image is formed from the light that goes from the candle to the mirror, is reflected, and then passes through the lens.

Where is the image? (S1, S2)

Explanation / Answer

for mirror

location of image is at center of curvature and inverted

i.e 26 cm from mirror

for lens candle and the image formed by mirror is at same location

so image formed by lens is:

Lens formula

1/f= 1/v – 1/u

f= 30.5cm [it is positive because f is right side of lens]

u= -85cm [it is negative because object is left side of lens]

1/v= 1/f +1/u =1/ 30.5 + 1/ (-85)

v= 47,57 cm right side of lens

hence image s1 & s2 both are at same position 47.57 and same height but one is erect and anothe is inverted

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