When an object is placed at a distance of 40 cm from a concave mirror the size of the image is 14 that of the object?

Join NOW to get access to exclusive study material for best results

Uh-Oh! That’s all you get for now.

We would love to personalise your learning journey. Sign Up to explore more.

Sign Up or Login

Skip for now

Uh-Oh! That’s all you get for now.

We would love to personalise your learning journey. Sign Up to explore more.

Sign Up or Login

Skip for now

Option 2 : 36 cm away from the mirror

India's Super Teachers for all govt. exams Under One Roof

Enroll For Free Now

Concept-

• The optical instrument which reflects the light and make the image of the object is called as mirror.
• The mirror having spherical curved reflecting surface is called as spherical mirror.

There are two types of spherical mirror:

1. Concave mirror:

• The spherical mirror having inward reflecting surface is called as concave mirror.
• The images form by the concave mirror can be real as well as virtual.

2. Convex mirror:

• The mirror whose reflecting surface is outward is called as convex mirror.
• The images form by the convex mirror is always virtual.

The mirror formula is given by:

\(\frac{1}{u} + \frac{1}{v} = \frac{1}{f}\)

Where u is object distance, v is image distance and f is focal length of the mirror

Explanation-

Given that:

Object distance (u) = - 40 cm

Focal length of the concave mirror (f) = - 15 cm

Use mirror formula:

\(\frac{1}{u} + \frac{1}{v} = \frac{1}{f}\)

\(\frac{1}{{ - 40}} + \frac{1}{v} = \frac{1}{{ - 15}}\)

\(\frac{1}{v} = \frac{1}{{40}} - \frac{1}{{15}} = \frac{{3 - 8}}{{120}} = \frac{{ - 5}}{{120}} = - \frac{1}{{24}}\)

Image distance (v) = - 24 cm

Now object is displaced through a distance of 20 cm towards the mirror;

New object distance (u’) = - (40 - 20) = - 20 cm

Focal length (f) = -15 cm

Use mirror formula:

\(\frac{1}{u} + \frac{1}{v} = \frac{1}{f}\)

\(\frac{1}{{ - 20}} + \frac{1}{{v'}} = \;\frac{1}{{ - 15}}\)

\(\frac{1}{{v'}} = \frac{1}{{20}} - \frac{1}{{15}} = \frac{{3 - 4}}{{60}} = - \frac{1}{{60}}\)

New image distance (v’) = - 60 cm

India’s #1 Learning Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Get Started for Free Download App

Trusted by 3.3 Crore+ Students

Text Solution

Solution : Givenn u=40 cm (negative) <br> `m=1/4` (negative for the real image) <br> a. From `m=-v/u,-1/4=-v/((-40))` or v=-10 cm <br> Thus the image is formed at a distance 10 cm in front of the mirror. <br> b. Now from relation `1/u+1/v=1/f` <br> `1/f=1/((-40))+1/((-10))` <br> `=(-5)/40` <br> or `f=(-40)/5=-8cm` <br> i.e., the focal length of concave mirror is 8cm.