An object is placed at a distance of 40 cm from a convex spherical mirror as shown in figure. T

step 1 Hello and welcome to this video solution of numerate. Here we are given object distance. U is eq

An object is placed at a distance of 40 cm from a convex...

An object is placed at a distance of $40 \mathrm{~cm}$ from a convex spherical mirror as shown in figure. The radius ofcurvature of the convex mirror is $20 \mathrm{~cm}$. At what distance from the object a plane mirror should be placed so that the image in the spherical mirror and plane mirror may be in one plane? (a) $20 \mathrm{~cm}$ (b) $24 \mathrm{~cm}$ (c) $28 \mathrm{~cm}$ (d) $32 \mathrm{~cm}$

An object is placed at a distance of $40 \mathrm{~cm}$ from a convex spherical mirror as shown in figure. The radius ofcurvature of the convex mirror is $20 \mathrm{~cm}$. At what distance from the object a plane mirror should be placed so that the image in the spherical mirror and plane mirror may be in one plane?
(a) $20 \mathrm{~cm}$
(b) $24 \mathrm{~cm}$
(c) $28 \mathrm{~cm}$
(d) $32 \mathrm{~cm}$

Key Concepts

Image Formation in Compound Mirror Systems

When combining plane and spherical mirrors, it is important to analyze how each mirror forms its image and under what geometric conditions images can coincide. This involves tracing the paths of light rays and ensuring that images from different mirrors align or appear to be in the same plane.

Mirror Equation

The mirror equation, 1/f = 1/u + 1/v, is fundamental in optics for relating the object distance (u), the image distance (v), and the focal length (f) of a mirror. It is used to determine where an image will form given a particular object position and mirror curvature.

Focal Length of Spherical Mirrors

The focal length (f) of a spherical mirror is directly related to its radius of curvature (R), with the relationship f = R/2 for spherical mirrors. This concept is crucial for determining image positions and sizes in various mirror systems.

Virtual Image Formation in Convex Mirrors

Convex mirrors always produce virtual, upright, and reduced images regardless of the object distance. Understanding the nature of these images, including how sign conventions apply in the mirror equation, is essential when analyzing optical systems involving convex mirrors.

Plane Mirror Reflection

Plane mirrors create images that are virtual, upright, and of the same size as the object, with the image distance equal to the object distance from the mirror. This principle is key when combining reflections from different types of mirrors in optical setups.

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