KVPY SX SB Exam 19-Nov-2017 Question Paper

Question : 98 of 120

Marks: +1, -0

Back surface of a glass (refractive index n and thickness t) is polished to work as a mirror as shown below. A laser beam falls on it and is partially reflected and refracted at the air-glass interface and fully reflected at the mirror surface respectively. A pattern of discrete spots of light is observed on the screen.

The spacing between the spots on the screenwill be

${2t \cosθ}/√{n^2-\sin^2θ}$
${2t \sinθ}/√{n^2-\sin^2θ}$
${2t \tanθ}/√{n^2-\sin^2θ}$
${2t \sinθ}/√{1- {\sin^2θ}/n^2}$

Validate

Solution:

Therefore

∆x = h_1 -h_2

\tanθ=d/h_1\ &\ \tan θ={d-L}/h^2

∆x=d/{\tanθ}-{d-L}/{\tanθ}

∆x=L/{\tanθ}

Snell's Law

1 - \sinθ = n-\sin r

⇒ 1 \sin r = {\sinθ}/n

\tan r = L/{2.t}⇒L = 2 t \tan r

L ={2t .\sinθ}/√{n^2-\sin^2θ}

∴

∆x={2t \sinθ}/{√{n^2-\sin^2θ}\tanθ}

\tanθ={2t \cosθ }/√{n^2-\sin^2θ}

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