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# solve

If t is thickness of glass slab of refractive index μ, it produces a shift  t[ 1 -(1/μ) ] in the path of travelling direction.
Hence slab of thickness 3 cm with refractive index (3/2) produes a shift 3[1-(2/3)] = 1 cm and
the object-to-mirror distance 16 cm becomes 15 cm because of glass slab.

virtual image is formed at a distance v behind the mirror as per mirror equation (1/u)+(1/v) = (1/f)

Hence  (-1/15)+(1/v) = (1/10)  or  v = 6 cm  behind the mirror.

now object-to-image distance 16+6 = 22 cm is getting shifted due glass slab by 1 cm, hence the distance becomes 21 cm

if d cm  is the distance between front surface of glass slab and object, we get image
due to partial reflection d cm behind the front surface of glass slab.

If two images are getting overlapped, then we have 2d = 21 or  d = 10.5 cm
Answered by Expert 11th May 2019, 11:21 AM
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