Captain Jack Sparrow tries to observe a fish | vedclass

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

Question

(A) For a medium with a variable refractive index $\mu(y)$,the apparent depth $h_{app}$ is given by the integral of the ratio of the infinitesimal dep

Vedclass · Accepted Answer

$\frac{\pi}{4} \ m$

Vedclass · Answer

(A) For a medium with a variable refractive index $\mu(y)$,the apparent depth $h_{app}$ is given by the integral of the ratio of the infinitesimal depth element $dy$ to the refractive index at that depth: $h_{app} = \int_{0}^{h} \frac{dy}{\mu(y)}$ Given $\mu(y) = y^2 + 1$ and the actual depth $h = 1 \ m$,we substitute these into the integral: $h_{app} = \int_{0}^{1} \frac{dy}{y^2 + 1}$ Using the standard integral formula $\int \frac{dx}{x^2 + 1} = 	an^{-1}(x) + C$,we get: $h_{app} = [	an^{-1}(y)]_{0}^{1}$ $h_{app} = 	an^{-1}(1) - 	an^{-1}(0)$ $h_{app} = \frac{\pi}{4} - 0 = \frac{\pi}{4} \ m$ Thus,the apparent depth is $\frac{\pi}{4} \ m$.

Similar Questions

$A$ ray of light passes through four transparent media with refractive indices $\mu_1, \mu_2, \mu_3$ and $\mu_4$ as shown in the figure. The surfaces of all media are parallel. If the emergent ray $CD$ is parallel to the incident ray $AB$,we must have

$A$ ray of light is incident at $30^{\circ}$ from a medium of refractive index $2$ into a medium of refractive index $1$. The angle of refraction is: (in $^{\circ}$)

$A$ beam of white light is partially reflected and partially refracted from a surface. The angle between the reflected and refracted light is $90^{\circ}$. The angle of refraction is $30^{\circ}$. The angle of incidence must be (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module