A point source is placed at a distance of 30cm from a convex lens (f=15cm). A glass slab of thickness 1cm is kept just in the opposite side of the lens. The refractive index of glass is 1.5. what will be image distance from lens?

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Answer 1 · 2018-08-10T21:14:27

$30.33 cm$

Suppose,the glass slab was absent,then the picture would have been like this,

enter image source here

So,applying lens formula,

$1/u - 1/v =1/f$

Given, $u=-30 cm, f=+15 cm$

Putting we get,

$v=30cm$

So,in absence of the glass slab,image would have been formed at $30 cm$ from the optical centre of the convex lens.

Now,if we consider a slab only,the ray diagram appears as follows,

enter image source here

so ,we can find a lateral shift of $x$ (dotted line represents the pathway of light which would have been traced if slab was not there)

Now,this lateral shift is given by the formula, $x=r- r/(mu)$

Given, $r=1 cm$ and $mu=1.5$

so, $x=0.33 cm$

Now,putting the lens and the slab together as wanted in the question,the reconstructed diagram looks like this,

enter image source here

So, now we can say that the image will be formed $v+x=30+0.33=30.33cm$ away from the optical centre of the convex lens.