Light travels a distance in time in air and in time in another denser medium. What is the critical angle for this medium? [2023]

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Q.
Light travels a distance $x$ in time $t_{1}$ in air and $10 x$ in time $t_{2}$ in another denser medium. What is the critical angle for this medium [2023]

1 $\sin^{- 1} (\frac{t_{1}}{10 t_{2}})$

2 $\sin^{- 1} (\frac{10 t_{1}}{t_{2}})$

3 $\sin^{- 1} (\frac{t_{2}}{t_{1}})$

4 $\sin^{- 1} (\frac{10 t_{2}}{t_{1}})$

Ans.
(2)

For air, $c = \frac{x}{t_{1}}$

For medium, $v = \frac{10 x}{t_{2}}; μ = \frac{c}{v} = \frac{x \times t_{2}}{t_{1} \times 10 x} = \frac{t_{2}}{10 t_{1}}$

$\sin C = \frac{1}{μ} = \frac{10 t_{1}}{t_{2}}; C = \sin^{- 1} [\frac{10 t_{1}}{t_{2}}]$

Solution

Q.
Light travels a distance $x$ in time $t_{1}$ in air and $10 x$ in time $t_{2}$ in another denser medium. What is the critical angle for this medium [2023]

1 $\sin^{- 1} (\frac{t_{1}}{10 t_{2}})$

2 $\sin^{- 1} (\frac{10 t_{1}}{t_{2}})$

3 $\sin^{- 1} (\frac{t_{2}}{t_{1}})$

4 $\sin^{- 1} (\frac{10 t_{2}}{t_{1}})$

Ans.
(2)

For air, $c = \frac{x}{t_{1}}$

For medium, $v = \frac{10 x}{t_{2}}; μ = \frac{c}{v} = \frac{x \times t_{2}}{t_{1} \times 10 x} = \frac{t_{2}}{10 t_{1}}$

$\sin C = \frac{1}{μ} = \frac{10 t_{1}}{t_{2}}; C = \sin^{- 1} [\frac{10 t_{1}}{t_{2}}]$

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Solution

Q. Light travels a distance x in time t1 in air and 10x in time t2 in another denser medium. What is the critical angle for this medium [2023]

1 sin-1(t110t2)

2 sin-1(10t1t2)

3 sin-1(t2t1)

4 sin-1(10t2t1)

Ans. (2) For air, c=xt1 For medium, v=10xt2 ; μ=cv=x×t2t1×10x=t210t1 sinC=1μ=10t1t2 ; C=sin-1[10t1t2]

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Q.
Light travels a distance $x$ in time $t_{1}$ in air and $10 x$ in time $t_{2}$ in another denser medium. What is the critical angle for this medium [2023]

1 $\sin^{- 1} (\frac{t_{1}}{10 t_{2}})$

2 $\sin^{- 1} (\frac{10 t_{1}}{t_{2}})$

3 $\sin^{- 1} (\frac{t_{2}}{t_{1}})$

4 $\sin^{- 1} (\frac{10 t_{2}}{t_{1}})$

Ans.
(2)

For air, $c = \frac{x}{t_{1}}$

For medium, $v = \frac{10 x}{t_{2}}; μ = \frac{c}{v} = \frac{x \times t_{2}}{t_{1} \times 10 x} = \frac{t_{2}}{10 t_{1}}$

$\sin C = \frac{1}{μ} = \frac{10 t_{1}}{t_{2}}; C = \sin^{- 1} [\frac{10 t_{1}}{t_{2}}]$