A candle is at the center of curvature of a concave mirror whose focal length is

Question

A candle is at the center of curvature of a concave mirror whose focal length is 10.0 cm. The converging lens has a focal length of 32.0 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. (a) For each of these two images, draw a principal-ray diagram that locates the image. (b) For each image, answer the following questions: (i) Where is the image? (ii) Is the image real or virtual? (iii) Is the image erect or inverted with respect to the original object?

Please show work. Thanks

Explanation / Answer

i) 1/s + 1/s' = 1/f

1/85.0 + 1/s' = 1/32

s' = 51.3 cm [to the right of the lens]

ii) image is real

iii) image is inverted

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1/s + 1/s' = 1/f

1/20 + 1/s' = 1/10

s' = 20 cm

so image from the mirror becomes the new object for the lens, is at the same location as the object.

so final image position is 51.3 cm to the right of lens

ii) image is real

iii) erect image

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