In an experiment,a convex lens of focal lengt | vedclass

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

Question

(A) Given: Focal length of the lens $f_l = 15 \, cm$,object distance $u = -20 \, cm$.Using the lens formula,$\frac{1}{f_l} = \frac{1}{v} - \frac{1}{u}

Vedclass · Accepted Answer

$27.5$

Vedclass · Answer

(A) Given: Focal length of the lens $f_l = 15 \, cm$,object distance $u = -20 \, cm$.Using the lens formula,$\frac{1}{f_l} = \frac{1}{v} - \frac{1}{u}$.$\frac{1}{v} = \frac{1}{15} - \frac{1}{20} = \frac{4-3}{60} = \frac{1}{60}$.So,$v = 60 \, cm$. The image is formed $60 \, cm$ to the right of the lens.For the object and image to coincide,the rays must strike the convex mirror normally. This happens if the rays are directed towards the center of curvature $(C)$ of the convex mirror.The distance of the mirror from the lens is $d = 5 \, cm$. The distance of the center of curvature from the mirror is $R = 2f_m$.The image formed by the lens is at a distance of $60 \, cm$ from the lens. Since the mirror is $5 \, cm$ from the lens,the distance of the image from the mirror is $60 - 5 = 55 \, cm$.Thus,the radius of curvature $R = 55 \, cm$.Since $R = 2f_m$,the focal length of the convex mirror is $f_m = \frac{R}{2} = \frac{55}{2} = 27.5 \, cm$.

Similar Questions

$A$ plano-convex lens $(f = 20 \ cm)$ is silvered at the plane surface. Now,the new focal length $F$ will be........$cm$.

When the plane surface of a plano-convex lens is silvered,it behaves as a concave mirror of focal length $60 \ cm$. However,when the convex surface is silvered,it behaves as a concave mirror of focal length $20 \ cm$. What is the refractive index of the lens?

$A$ prism having a refractive index $1.414$ and a refracting angle $30^{\circ}$ has one of its refracting surfaces silvered. $A$ beam of light incident on the other refracting surface will retrace its path if the angle of incidence is: (in $^{\circ}$)

$A$ plano-convex lens,when silvered on the plane side,behaves like a concave mirror of focal length $30 \ cm$. However,when silvered on the convex side,it behaves like a concave mirror of focal length $10 \ cm$. The refractive index of its material is:

$A$ plano-convex lens made of material of refractive index $\mu$ with radius of curvature $R$ is silvered on the curved side. How far away from the lens-mirror must you place a point object,so that the image coincides with the object?

Vedclass Test Series

Exam Paper Generator

Online Exam Module