EFFECTS OF REFRACTION

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EFFECTS OF REFRACTIONS:

(a) The apparent depth of objects is lesser in denser media than the actual depth because of this, Swimming pool appears to be much smaller than it actually is.

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Explanation: Let us consider a object ‘O’ lying at the bottom of a beaker containing water. Two rays ‘OA’ and ‘OB’ from object ‘O’ are refracted along ‘AD’ and ‘BC’ respectively. These divergent rays appear to come from ‘I’ which is virtual image of object ‘O’.

From snell’s law, \frac{{\sin \,i}}{{\sin \,r}} = {n_{aw}}

or \,\frac{{\sin \,r}}{{\sin \,i}} = {n_{wa}}

For small angles, \sin \,i\, \simeq \,\tan \,i\, = \,\frac{{AB}}{{OA}}

\sin \,r\, \simeq \,\tan \,r\, = \,\frac{{AB}}{{O'A}}

Put in equation (1)

\frac{{AB/O'A}}{{AB/OA}} = {n_{wa}}

\frac{{OA}}{{O'A}} = {n_{wa}}

\begin{array}{l} \frac{{RD}}{{AD}}\, = \,{n_{wa}}\\ AD\, = \,\frac{{RD}}{n} \end{array}

APPARENT SHIFT

\begin{array}{l} Apparent\,shift\, = \,RD - AD = RD - \frac{{RD}}{n}\\ = RD\left[ {1 - \frac{1}{n}} \right] \end{array}

APPARENT DEPTH OF A NUMBER OF IMMISCIBLE LIQUIDS

If a vessel is filled with three immiscible liquids of refractive indices{n_1}, {n_2}and{n_3}, then the apparent depth is given by:

AD = \frac{{{d_1}}}{{{n_1}}} + \frac{{{d_2}}}{{{n_2}}} + \frac{{{d_3}}}{{{n_3}}}

Where {d_1},\,{d_2}and {d_3}represent the heights of liquids.

Generalising, AD = \frac{{{d_1}}}{{{n_1}}} + \frac{{{d_2}}}{{{n_2}}} + \frac{{{d_3}}}{{{n_3}}} + ............... + \frac{{{d_n}}}{{{n_n}}}

Or AD = \sum\limits_{i = 1}^n {\frac{{{d_i}}}{{{n_i}}}}

NOTE:

· If the observer is in denser medium and object is in rarer medium, then n < 1. Therefore AD > RD. Thus for a fish, the bird appears to be higher than its actual height.

(a) Delayed sunset and advanced sunrise: The sun is visible before actual sunrise and after actual sunset because of atmospheric refraction.

By actual sunrise we mean the actual crossing of the horizon by the sun. the refractive index of air w.r.t vacuum is 1.00029, during this the apparent shift in the direction of the sun is about 0 .5° and the corresponding time difference between actual sunset and apparent sunset is about 2 minutes.

The apparent flattening of the sun at sunset and sunrise also is due to the same reason.

(b) Twinkling of stars:

It is also caused due to refraction by different layers of air of different densities and different refractive index.

The paths of light therefore undergo continuous changes and the stars appear at different places, very near to their actual position.

(c) A straight rod appears bent in water.

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(d) The stars seem higher than they actual are.

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