An electric lamp is fixed at the ceiling of a | vedclass

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

Question

(D) Let the radius of the circular tunnel be $r$. The lamp is at the top of the tunnel. The distance of point $A$ from the lamp is $2r$.Intensity at $

Vedclass · Accepted Answer

$1:\sqrt{2}$

Vedclass · Answer

(D) Let the radius of the circular tunnel be $r$. The lamp is at the top of the tunnel. The distance of point $A$ from the lamp is $2r$.Intensity at $A$ is $I_A = \frac{L}{(2r)^2} = \frac{L}{4r^2}$,where $L$ is the luminous intensity of the lamp.For point $B$,the distance from the lamp is $d = \sqrt{r^2 + r^2} = r\sqrt{2}$. The angle $	heta$ between the normal at $B$ and the light ray is $45^\circ$.Intensity at $B$ is $I_B = \frac{L}{d^2} \cos 	heta = \frac{L}{(r\sqrt{2})^2} \cos 45^\circ = \frac{L}{2r^2} \cdot \frac{1}{\sqrt{2}} = \frac{L}{2\sqrt{2}r^2}$.Therefore,the ratio is $\frac{I_A}{I_B} = \frac{L/4r^2}{L/2\sqrt{2}r^2} = \frac{2\sqrt{2}}{4} = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}$.

An electric lamp is fixed at the ceiling of a circular tunnel as shown in the figure. What is the ratio of the intensities of light at base $A$ and a point $B$ on the wall?

Similar Questions

Discuss the sign convention of distances for reflection by a spherical mirror and refraction by a spherical lens.

$A$ lamp is hanging $1 \, m$ above the center of a circular table of diameter $1 \, m$. The ratio of illuminances at the center and the edge is:

$A$ convex lens forms an image of an object on a screen. The height of the image is $9 \, cm$. The lens is now displaced until an image is again obtained on the screen. The height of this image is $4 \, cm$. The distance between the object and the screen is $90 \, cm$.

Two light sources with equal luminous intensity are placed at a distance of $1.2\, m$ from each other. Where should a screen be placed between them such that the illuminance on one of its faces is four times that on the other face?

In the figure shown,a point object $O$ is placed in air on the principal axis. The radius of curvature of the spherical surface is $60\, cm$. Let $I_f$ be the final image formed after all the refractions and reflections. Which of the following statements is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module