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Q.

A convex mirror and a concave mirror of radius 10 cm each are placed 15 cm apart facing each other. An object is placed midway between them. If the reflection first takes place in the concave mirror and then in convex mirror, the position of the final image is:

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a

On the pole of the convex mirror

b

On the pole of the concave mirror

c

At a distance of 10cm from the convex mirror

d

At a distance of 5cm from the convex mirror

answer is A.

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Detailed Solution

Concept- A mirror's focal length is defined as its radius. The focal length for a concave mirror is regarded as negative. The item is positioned directly in the center of the two lenses, dividing the distance between them by two evenly, which is 15 cm.
The item in this instance is 'O,' and it is positioned midway between the two mirrors.
We are aware of that concave mirror.

u 1 = − 7.5

and

f 1 = − 5

On applying mirror formulae,

1 f 1 = 1 v 1 + 1 u 1

⇒ 1 v 1 − 215 = − 1 5

v 1 = − 15

We may infer from the value of v that the picture is created at the pole of the convex mirror.
In relation to the convex mirror,

u 2 = 0

and

f 2 = + 5

On applying mirror formulae,

⇒ 1 f 2 = 1 v 2 + 1 u 2

⇒ 1 v 2 + 10 = 15

⇒ v 2 = 0

Thus, the convex mirror's pole is where the final picture is generated.
Hence, the correct option is 1.

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