In the displacement method,a convex lens is p | vedclass

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

Question

(B) In the displacement method,for a fixed distance $D$ between the object and the screen,there are two positions of the lens where a sharp image is f

Vedclass · Accepted Answer

$\frac{x}{m_1 - m_2}$

Vedclass · Answer

(B) In the displacement method,for a fixed distance $D$ between the object and the screen,there are two positions of the lens where a sharp image is formed.Let the object distance be $u$ and image distance be $v$ for the first position. Then $m_1 = v/u$.For the second position,by the principle of reversibility,the object distance becomes $v$ and the image distance becomes $u$. Thus,$m_2 = u/v$.Note that $m_1 	imes m_2 = (v/u) 	imes (u/v) = 1$.Given the displacement of the lens is $x = v - u$.We know $m_1 - m_2 = v/u - u/v = (v^2 - u^2) / (uv) = (v - u)(v + u) / (uv) = x(v + u) / (uv)$.From the lens formula,$1/f = 1/v - 1/(-u) = (u + v) / (uv)$.Substituting this into the expression for $m_1 - m_2$,we get $m_1 - m_2 = x 	imes (1/f) = x/f$.Therefore,the focal length $f = x / (m_1 - m_2)$.

In the displacement method,a convex lens is placed between an object and a screen. If the magnifications in the two positions are $m_1$ and $m_2$ and the displacement of the lens between the two positions is $x$,then the focal length of the lens is:

Similar Questions

The size of the images of an object, formed by a thin lens, are equal when the object is placed at two different positions $8 \ cm$ and $24 \ cm$ from the lens. The focal length of the lens is . . . . . . $cm$.

If the focal lengths of red and violet light rays for the same lens are $f_R$ and $f_v$ respectively,then which of the following is true?

In the diagram shown,the lens is moving towards the object with a velocity $V \, m/s$ and the object is also moving towards the lens with the same speed. What is the speed of the image with respect to the earth when the object is at a distance $2f$ from the lens? ($f$ is the focal length.)

$A$ beam of light converges at a point $P$. Now a lens is placed in the path of the convergent beam $12 \, cm$ from $P$. At what point does the beam converge if the lens is a concave lens of focal length $16 \, cm$ (in $, cm$)?

The refractive index of the material of a double convex lens is $1.5$ and its focal length is $5 \,cm$. If the radii of curvature are equal, the value of the radius of curvature (in $cm$) is

Vedclass Test Series

Exam Paper Generator

Online Exam Module