A prism with a refractive index of 1.53 is pl | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given: Refractive index of glass with respect to air $^{a}\mu_{g} = 1.53$,refractive index of water with respect to air $^{a}\mu_{w} = 1.33$,and p

Vedclass · Accepted Answer

$10.2$

Vedclass · Answer

(C) Given: Refractive index of glass with respect to air $^{a}\mu_{g} = 1.53$,refractive index of water with respect to air $^{a}\mu_{w} = 1.33$,and prism angle $A = 60^{\circ}$.The refractive index of the prism with respect to water is given by:$^{w}\mu_{g} = \frac{^{a}\mu_{g}}{^{a}\mu_{w}} = \frac{1.53}{1.33} \approx 1.15$.The formula for the angle of minimum deviation $\delta_{m}$ is:$^{w}\mu_{g} = \frac{\sin(\frac{A + \delta_{m}}{2})}{\sin(\frac{A}{2})}$.Substituting the values:$1.15 = \frac{\sin(\frac{60^{\circ} + \delta_{m}}{2})}{\sin(30^{\circ})}$.Since $\sin(30^{\circ}) = 0.5$:$\sin(\frac{60^{\circ} + \delta_{m}}{2}) = 1.15 	imes 0.5 = 0.575$.Taking the inverse sine:$\frac{60^{\circ} + \delta_{m}}{2} = \sin^{-1}(0.575) \approx 35.1^{\circ}$.Solving for $\delta_{m}$:$60^{\circ} + \delta_{m} = 70.2^{\circ} \implies \delta_{m} = 10.2^{\circ}$.

$A$ prism with a refractive index of $1.53$ is placed in water with a refractive index of $1.33$. If the angle of the prism is $60^{\circ}$,then the angle of minimum deviation in water will be ....$^{\circ}$.

Similar Questions

For a glass prism $(\mu = \sqrt{3})$,the angle of minimum deviation is equal to the angle of the prism. Find the angle of the prism. (in $^{\circ}$)

The variation of the refractive index of a crown glass thin prism with the wavelength of the incident light is shown. Which of the following graphs is the correct one,if $D_m$ is the angle of minimum deviation?

Two thin prisms of flint glass, with refracting angles of $6^o$ and $8^o$ respectively, possess dispersive powers in the ratio

The angle of a prism is $60^{\circ}$ and the angle of minimum deviation is $30^{\circ}$. The angle of incidence is ........$^{\circ}$.

$A$ yellow light undergoes minimum deviation through a prism. If $i_1$ and $i_2$ are the angle of incidence and the angle of emergence respectively,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module