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

For image formed directly through lens

Using the equation,

1/o + 1/f = 1/i

where o = object's distance = -85 cm

f = focal length = 30.58 cm

So, 1/i = 1/(-85) + 1/(30.58)

So, i = 47.76 cm = s1 <----answer

For the image from the mirror,

1/o + 1/f = 1/i

So, 1/(-2*8.4) + 1/(8.4) = 1/i

So, i = 16.8 cm

Now, for this virtual image, using the lens formula,

1/o + 1/f = 1/i

1/(85) + 1/30.58 = 1/i

So, i = s2 = 22.49 cm <------answer

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