Question

A Light Ray is incident at an angle 45 degree on parallel sided glass slab and emerged out grazing the vertical surface. The refractive index of the slab is
a) root 3/2 b) root 5/2 c) root only on 3 divided by 2 d) root only to 5 divided by 2

Answer 1

Answer:

Explanation:

Using Snell's law,

μ=sinisinr

Also, since, it is at grazing angle,r=90−c

Thus, μ=sinicosc

From the definition of critical angle, sinc=1μ

Also, cosc=√1−sin2c

Thus, putting in all the values and i=45

,

we get μ=√32

Answer 2

Answer:

The refractive index of the slab is $\sqrt{\frac{3}{2} }$ i.e.option(A).

Explanation:

From the snell's law, we have,

$\mu=\frac{sini}{sinr}$      (1)

Where,

μ=refractive index of glass slab

i=angle of incidence

r=angle of refraction

From the question we have,

The angle of incidence(i)=45°

The angle of refraction(r)=90°-C       (As it is at grazing angle)

C=critical angle

By putting the value of "r" in equation (1) we get;

$\mu=\frac{sini}{sin(90\textdegree - C)}$

$\mu=\frac{sini}{cos C}$        (2)

And we know that,

$SinC=\frac{1}{\mu}$      (3)

Also,

$cosC=\sqrt{1-sin^2C}$     (4)

By putting the value of "SinC" in equation (4) we get;

$cosC=\sqrt{1-(\frac{1}{\mu})^2 }$      (5)

Now by substituting the value of CosC and "i" in equation (2) we get;

$\mu=\frac{sin45\textdegree}{\sqrt{1-(\frac{1}{\mu})^2 }}$

$\mu\times \sqrt{1-(\frac{1}{\mu})^2 } =\frac{1}{\sqrt{2} }$

$\mu\times \frac{\sqrt{\mu^2-1} }{\mu}=\frac{1}{\sqrt{2} }$

$\mu^2-1=\frac{1}{2}$

$\mu^2=\frac{1}{2}+1$

$\mu^2=\frac{3}{2}$

$\mu=\sqrt{\frac{3}{2}}$

Hence, the refractive index of the slab is $\sqrt{\frac{3}{2} }$ i.e.option(A).

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