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Rectilinear Propagation of Light

Light follows...

Question

Light follows a curved path in the same medium because it is the shortest path to go from one point to another and takes minimum time.

A

True

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B

False

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Solution

The correct option is B False
Light always travels in a straight line.
Light changes its path when it enters from one medium to another medium.
Hence, the given statement is false.

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Q. Pierre de Fermat

(1601 - 1665)

showed that whenever light travels from one point to another, its actual path is the path that requires the smallest time interval. This statement is known as Fermat's principle. The simplest example is for light propagating in a homogeneous medium. It moves in a straight line because a straight line is the shortest distance between two points. Derive Snell's law of refraction from Fermat's principle. Proceed as follows. In this Figure. a light ray travels from point

P

in medium 1 to point

Q

2 .

The two points are, respectively, at perpendicular distances

a

b

from the interface. The displacement from

P

Q

has the component

d

parallel to the interface, and we let

x

represent the coordinate of the point where the ray enters the second medium. Let

t = 0

be the instant the light starts from

P

.
(a) Show that the time at which the light arrives at

Q

t = \frac{r_{1}}{v_{1}} + \frac{r_{2}}{v_{2}} = \frac{n_{1} \sqrt{a^{2} + x^{2}}}{c} + \frac{n_{2} \sqrt{b^{2} + (d - x)^{2}}}{c}

(b) To obtain the value of

x

t

has its minimum value, differentiate

t

with respect to

x

and set the derivative equal to zero. Show that the result implies

\frac{n_{1} x}{\sqrt{a^{2} + x^{2}}} = \frac{n_{2} (d - x)}{\sqrt{b^{2} + (d - x)^{2}}}

(c) Show that this expression in turn gives Snell's law,

n_{1} sin θ_{1} = n_{2} sin θ_{2}

Q. Light travelling in a from one point to another follows the path such thay time taken by it is a) minimum b) maximum c) optimum d) none

Q. Statement I : A light ray follows rectilinear propagation even when it travels in different media.
Statement II : A light ray would always choose the shortest path to travel from one point to another.

Why does a ray of light travelling from one medium to another change its path?

Bending of light from its original path while traveling from one medium to another is called:

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