A thin, diverging lens having a focal length of magnitude 45.0 cm has the same p

Question

A thin, diverging lens having a focal length of magnitude 45.0 cm has the same principal axis as a concave mirror with a radius of 60.0 cm. The center of the mirror is 20.0 cm from the lens, with the lens in front of the mirror. An object is placed 15.0 cm in front of the lens. (a) (a) Where is the final image due to the lensmirror combination? (b) Is the final image real or virtual? Upright or inverted?

The answer to part a) is 7.5 x 10^2 but I have no idea how to get that answer, along with the answer to part b

Explanation / Answer

Here image formed by the diverging lense will work as the object for the concave mirror so first we try to find out the distance of image formed by diverging lense.

For diverging lense

distance of object d0=15 cm and focal length f=-45 cm

distance of image di = ?

Now using

1/f=1/do + 1/di

-1/45 = 1/15 + 1/di

1/di=-0.089

di=-11.24 cm

Now this image is formed is in the same side of the object .

Now for concave lense

di=?

do=20+11.24 =31.24 cm

f=30 cm

using

1/di + 1/do =1/f

1/di + 1/(31.24) = 1/30

1/di=0.001323

di=755.85 cm ANS

(b) The formed image will be real and inverted.

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