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Q.

A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and a plane mirror are arranged as shown. For an object kept at a distance of 60cm from the convex lens, the final image, formed by the combination, is a real image, at a distance of: 

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a

70 cm from the concave lens

b

 60 cm from the concave lens

c

60 cm from the convex lens 

d

70 cm from the convex lens

answer is A.

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Detailed Solution

We can isolate each optical system for simple calculations even if there are several optical systems involved. The distance at which images are formed by concave and convex lenses may be determined using the lens formula. We must determine the actual picture location in this problem, not the virtual image position.

After first refraction from the lens, the first image formation is,

1v+160=130 

v=60cm

The refraction from the concave lens is 

1v2-140=-1120

v2=60cm

It forms behind the mirror; this will be final image.

It's a distance of 60 cm from the concave lens.

So, the image will form at 60 cm from the convex lens. Hence the option C is correct. In the diagram you can find this image at point v.

Hence, option 1 is correct.

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