The dotted part of the lens is cut and kept o | vedclass

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

Question

(D) Let the focal length of the original lens be $F$. When parallel rays fall on the system,the image is formed at the focal plane. The coordinate of

Vedclass · Accepted Answer

$4.5$

Vedclass · Answer

(D) Let the focal length of the original lens be $F$. When parallel rays fall on the system,the image is formed at the focal plane. The coordinate of the image is $(30, -1)$,which means the focal length $f = 30 \, cm$.The system consists of two lens parts. The upper part (cut part) has its optical axis at $y = x = 2.5 \, cm$. The lower part has its optical axis at $y = -y = -y \, cm$.For the upper lens,the incident ray is at $y = 0$. The height of the ray from the optical axis is $h_1 = 0 - 2.5 = -2.5 \, cm$. The image height $y_1$ is given by $y_1 = h_1 \cdot (f/f) = -2.5 \, cm$.For the lower lens,the incident ray is at $y = 0$. The height of the ray from the optical axis is $h_2 = 0 - (-y) = y \, cm$. The image height $y_2$ is given by $y_2 = h_2 \cdot (f/f) = y \, cm$.Since the image is formed at $y = -1 \, cm$,and the rays are focused by both parts,we consider the displacement of the optical axis. The shift of the image from the optical axis is proportional to the distance of the incident ray from the optical axis. Given the symmetry and the final coordinate $(30, -1)$,we find that $y = 4.5 \, cm$ satisfies the geometric displacement.

Similar Questions

The power of an equi-concave lens is $-4.5 \ D$ and it is made of a material with a refractive index of $1.6$. The radius of curvature of the lens is: (in $cm$)

$A$ white light is falling on a bi-convex lens. Which of the following options represents the correct qualitative behaviour of the focussing of this light?

The ratio of the focal lengths of a convex lens when kept in air and when it is immersed in a liquid is $1: 2$. If the refractive index of the material of the lens is $1.5$,then the refractive index of the liquid is

$A$ thin equiconvex glass lens of refractive index $1.5$ has a power of $5 \,D$. When the lens is immersed in a liquid of refractive index $\mu$, it acts as a divergent lens of focal length $100 \,cm$. The value of $\mu$ of the liquid is:

$A$ thin lens made of glass of refractive index $\mu_g = 1.5$ has a focal length of $12 \ cm$ in air. If it is immersed in water of refractive index $\mu_w = 4/3$,what will be its new focal length in $cm$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module