A ray of light travelling in a transparent medium of refractive index , falls on a surface separating the medium from air at an angle of incidence of $45^{o}$ . For which of the following value of refractive index the ray can undergo total internal reflection :

Question

A ray of light travelling in a transparent medium of refractive index , falls on a surface separating the medium from air at an angle of incidence of

45^{o}

. For which of the following value of refractive index the ray can undergo total internal reflection :

Toppr Admin · Accepted Answer

For total internal reflection-xA0-sin i -gt- sin c-xA0-where- i - angle of incidence- C - critical angle-xA0-But- sinC-1-x3BC-x2234-sini-1-x3BC-or-x3BC-1sini-x2234-x3BC-gt-1sin45or-x3BC-gt-x221A-2-i-45Given-Hence- option -c- is correct-

A ray of light travelling in a transparent medium of refractive index μ, falls on a surface separating the medium from air at an angle of incidence of 45o . For which of the following value of μ the ray can undergo total internal reflection ?μ=1.33μ=1.50μ=1.25μ=1.40

For total internal reflection, sin i > sin c where, i = angle of incidence, C = critical angle But, sinC=1μ∴sini=1μorμ=1sini∴μ>1sin45orμ>√2(i=45Given)Hence, option (c) is correct.

For total internal reflection,
sin i > sin c
where, i = angle of incidence, C = critical angle

But, $s i n C = \frac{1}{μ} ∴ s i n i = \frac{1}{μ} o r μ = \frac{1}{s i n i}$

$∴ μ > \frac{1}{s i n 45} o r μ > \sqrt{2} (i = 45 G i v e n)$

Hence, option (c) is correct.