As shown in the figure (Figure 1) , a candle is at the center of curvature of a

Question

As shown in the figure (Figure 1) , a candle is at the center of curvature of a concave mirror whose focal length is 8.4cm . The converging lens has a focal length of 30.58cm and is 85cm 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.
For each image, answer the following questions:

Where is the image?

Enter your answer as two numbers separated with a comma.

Explanation / Answer

Solution: We know that for an object situated at the center of curvature of the concave mirror, the rays from the object falls normally on the mirror and retrace its path. So, the image will also be formed at the same position of the object itself.

Now, considering the converging lens, u = -85 cm. f = 30.58 cm. So, by using 1/v - 1/u = 1/f, we get v = 47.76 cm. The positive magnitude of v is indicating that the image is situated right to the converging lens.

Evidently, position of the first and second image will coincide as discussed before.

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