# A REAL OBJECT IS LOCATED IS LOCATED AT ZERO END OF A METER STICK. A CONCAVE MIRROR LOCATED AT 100 cm END OF THE METER STICK FORMS AN IMAGE OF THE OBJECT AT THE 70cm POSITION. A CONVEX MIRROR PLACED AT THE 60cm POSITION FORMS A FINAL IMAGE AT THE 10 cm POINT WHAT IS THE RADIUS OF CURVATURE OF THE CONVEX MIRROR?

### Asked by iraza2663 | 21st Apr, 2021, 09:18: AM

Expert Answer:

### As per given question , there is a image formed by concave mirror at 70 cm mark of metre scale
for the object placed at 0 cm mark of meter scale
Hence using mirror equation we find focal length of concave mirror as follows
Mirror equation :- (1/v) + (1/u) = 1/f
where v = 30 cm is mirror to image distance, u = 100 cm is mirror-to-object distance and f is focal length of mirror
Hence we have , (1/f) = (1/30) +(1/100) = 13/300
we get focal length f = 23.08 cm
This image at 70 cm mark acts as object for a convex mirror at 60 cm mark of meter scale .
Hence mirror-to-object distance is 10 cm only .
There is a convex mirror at 60 cm mark of metre scale .
Hence convex mirror will form virtual image of image formed by concave mirror at 70 cm mark .
This virtual image is acting object for concave mirror to get final image at 10 cm mark of metre scale.
To get final image at 10 cm mark by concave mirror ,we calculate object distance as follows
Mirror equation :- (1/v) + (1/u) = 1/f
now v = 90 cm and f = 23.08 cm
(1/u) = (13/300) - ( 1/90) = 29/900
Hence object distance from concave mirror to get final image = 900/29 = 31.03 cm
We should get above object distance greater than 40 cm because convex mirror is at a distance 40 cm from
mirror and the virtual image formed by convex mirror is at a distance greater than 40 cm from concave mirror.
Hence it appears this problem is not formulated properly

### Answered by Thiyagarajan K | 21st Apr, 2021, 04:32: PM

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