Question

A point object O is placed in front of a transparent slab at a distance x from its closer surface. It is seen from the other side fo the slab by light incident nearly normally to the slab. The thickness of the slab is t and its refractive index is μ. Show that the apparent shift in the position fo the object is independent of x and find its value.

Open in App

Solution

The correct option is **A** t(1−tμ),

The situation is shown in figure. Because of the refraction at the first surface, the image of O is formed at O1. For this refractiion, the real depth is AO = x and the apparent depth is AO1. Also the first medium is air and the second is the slab. Thus,

xAO1=1μor,AO1=μx.

The point O1 acts as the object for the refractiion at the second surface. Due to this refraction the image of O1 is formed at I. Thus,

BO1BI=μ

or, AB+AO1BI=μ or t+μxBI=μ

or BI=x+tμ.

The net shift in OI=OB−BI=(x+t)−(x+tμ)

=t(1−tμ),

which is independent of x.

The situation is shown in figure. Because of the refraction at the first surface, the image of O is formed at O1. For this refractiion, the real depth is AO = x and the apparent depth is AO1. Also the first medium is air and the second is the slab. Thus,

xAO1=1μor,AO1=μx.

The point O1 acts as the object for the refractiion at the second surface. Due to this refraction the image of O1 is formed at I. Thus,

BO1BI=μ

or, AB+AO1BI=μ or t+μxBI=μ

or BI=x+tμ.

The net shift in OI=OB−BI=(x+t)−(x+tμ)

=t(1−tμ),

which is independent of x.

0

View More