Light is incident on a parallel sided rectangular glass slab at 45 degrees on one face AB of the slab and emerges from the opposite face CD. What is the distance traveled by the light ray inside the glass if the thickness AC of the glass slab is 4cm and the refractive index of the material of the glass slab is $\sqrt{2}$ ?

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Solution

$s i n i = η s i n r \Rightarrow s i n 45 = \sqrt{2} s i n r \Rightarrow \frac{1}{2} = s i n r ∴ r = 30^{\circ} I n Δ A B C, c o s 30^{\circ} = \frac{A C}{A B} \Rightarrow \frac{\sqrt{3}}{2} = \frac{4}{A B} ∴ A B = \frac{8}{\sqrt{3}} c m$

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sini=ηsinr⇒sin45=√2sinr⇒12=sinr∴r=30∘InΔABC,cos30∘=ACAB⇒√32=4AB∴AB=8√3cm

$s i n i = η s i n r \Rightarrow s i n 45 = \sqrt{2} s i n r \Rightarrow \frac{1}{2} = s i n r ∴ r = 30^{\circ} I n Δ A B C, c o s 30^{\circ} = \frac{A C}{A B} \Rightarrow \frac{\sqrt{3}}{2} = \frac{4}{A B} ∴ A B = \frac{8}{\sqrt{3}} c m$