An object is placed at a distance of 45 cm from a converging lens of focal length 30cm. A convex mirror of radius of curvature 40cm is to be placed on the other side of the lens so that the object coincides with its image. Find the position of the mirror from the lens.
A.50 cm
B.60 cm
C.90 cm
D.30 cm
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Answer:
the answer will be
D. 30 cm
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Thus the position of the mirror from the lens is 50 cm
Explanation:
- The object and image will coincide only if light ray retraces its path and it will occur only when the ray normally strikes at mirror.
- In other words , the centre of curvature of mirror and rays incident on mirror are colinear.
- The rays after refraction from lens must be directed towards the centre of curvature of mirror at C.
If x is separation , then for lens
- u = −45 cm
- v = x+40
- f = 30 cm
Using lens formula
1v − 1u = 1f
or 1x+40−1−45=130
or x = 45(30) 45 − 30 − 40 = 50 cm
Thus the position of the mirror from the lens is 50 cm
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