An object is placed at a distance of 50 , cm | vedclass

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

Question

(D) The object is at a distance of $50 \, cm$ from the convex mirror. The plane mirror is placed at a distance of $30 \, cm$ from the object. Since th

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(D) The object is at a distance of $50 \, cm$ from the convex mirror. The plane mirror is placed at a distance of $30 \, cm$ from the object. Since the total distance from the object to the convex mirror is $50 \, cm$,the distance from the plane mirror to the convex mirror is $50 - 30 = 20 \, cm$. The plane mirror forms a virtual image of the object at a distance of $30 \, cm$ behind the plane mirror. The distance of this image from the convex mirror is $30 + 20 = 50 \, cm$ behind the mirror. However,the problem states there is no parallax,meaning the images formed by both mirrors coincide. The image formed by the plane mirror is at a distance of $30 \, cm$ behind the mirror. Looking at the geometry,the distance of the image formed by the plane mirror from the pole $P$ of the convex mirror is $v = 30 - 20 = 10 \, cm$ (behind the mirror). Thus,for the convex mirror,$u = -50 \, cm$ and $v = +10 \, cm$. Using the mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$: $\frac{1}{10} + \frac{1}{-50} = \frac{1}{f}$ $\frac{5 - 1}{50} = \frac{1}{f} \Rightarrow \frac{4}{50} = \frac{1}{f} \Rightarrow f = 12.5 \, cm$. The radius of curvature $R = 2f = 2 	imes 12.5 = 25 \, cm$.

Similar Questions

$A$ satisfactory photographic print is obtained when the exposure time is $10 \, s$ at a distance of $2 \, m$ from a $60 \, cd$ lamp. The time of exposure required for the same quality print at a distance of $4 \, m$ from a $120 \, cd$ lamp is $... \, s$.

Ray optics is valid when characteristic dimensions are:

Shown in the figure is a convergent lens placed inside a cell filled with a liquid. The lens has a focal length of $+20\,cm$ when in air and its material has a refractive index of $1.50$. If the liquid has a refractive index of $1.60$,the focal length of the system is......$cm$.

$A$ convex lens of focal length $30\,cm$,a concave lens of focal length $120\,cm$,and a plane mirror are arranged as shown. For an object kept at a distance of $60\,cm$ from the convex lens,the final image,formed by the combination,is a real image at a distance of:

Vedclass Test Series

Exam Paper Generator

Online Exam Module