A luminous object is separated from a screen | vedclass

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

Question

(D) For a convex lens to form a real image of an object on a screen separated by a fixed distance $d$,the condition for the existence of the image is

Vedclass · Accepted Answer

$\frac{d}{4}$

Vedclass · Answer

(D) For a convex lens to form a real image of an object on a screen separated by a fixed distance $d$,the condition for the existence of the image is given by the displacement method.Let $u$ be the object distance and $v$ be the image distance. Then $u + v = d$.For a real image,the lens formula is $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$.Substituting $u = -(d - v)$,we get $\frac{1}{v} + \frac{1}{d - v} = \frac{1}{f}$.This simplifies to the quadratic equation $v^2 - dv + df = 0$.For $v$ to have real roots,the discriminant must be non-negative: $D = d^2 - 4df \geq 0$.This implies $d^2 \geq 4df$,or $f \leq \frac{d}{4}$.Thus,the maximum possible focal length of the convex lens is $\frac{d}{4}$.

$A$ luminous object is separated from a screen by a distance $d$. $A$ convex lens is placed between the object and the screen such that it forms a distinct image on the screen. The maximum possible focal length of this convex lens is

Similar Questions

Find the magnification for the lens. The focal length is $25 \; cm$.

$A$ thin plano-convex lens of focal length $73.5 \ cm$ has a circular aperture of diameter $8.4 \ cm$. If the refractive index of the material of the lens is $\frac{5}{3}$,then the thickness of the lens is nearly

$A$ screen is placed $90\, cm$ from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by $20\, cm$. The focal length of the lens is.....$ cm$

Monochromatic light rays parallel to $x$-axis strike a convex lens $AB$. If the lens oscillates such that $AB$ tilts up to a small angle $\theta$ (in radian) on either side of $y$-axis,then the amplitude of oscillation of the image will be ($f =$ focal length of the lens):

Vedclass Test Series

Exam Paper Generator

Online Exam Module