NCERT Solution for Class 10 Science Chapter 10

Light – Reflection and Refraction

NCERT Books for Session 2022-2023

CBSE Board and UP Board

Intext Questions

Page No-171

Questions No-2

# A concave mirror produces three times magnified (enlarged) real image of an object placed at 10 cm in front of it. Where is the image located?

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Magnification produced by a spherical mirror is given by the relation,

m = Height of the image / Height of the Object = – Image distance / Object distance

m = h₁/h₀ = -v/u

Let the height of the object, ho = h

Then, height of the image, hI = −3h (Image formed is real)

-3h/h = -v/u

v/u = 3

Object distance, u = −10 cm v = 3 × (−10) = −30 cm

Here, the negative sign indicates that an inverted image is formed at a distance of 30 cm

in front of the given concave mirror.

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Because the image is real, so magnification m must be negative.

m = -v/u

-3 = -v/-10

v = -30

Thus the image is located at a distance of 30 cm from the mirror on the object side of the mirror.

Because the image is real, so magnification m must be negative.

m = -v/u

-3 = -v/-10

v = -30

Thus the image is located at a distance of 30 cm from the mirror.

m = − v/u= −3 or v = 3u

But u = -10

∴ v = −30cm.

To find the image location in a concave mirror, you can use the mirror formula:

1/f = 1/d_0 + 1/d₁

Where:

» f is the focal length of the mirror (positive for concave mirrors),

» d_o is the object distance (distance from the object to the mirror)

» d₁ is the image distance (distance from the image to the mirror).

Given that the concave mirror produces a magnified (enlarged) real image, the magnification (m) is positive and given by the formula:

m = – d₁/d_0

In this case, you’re told that the magnification is 3, so m = 3.

Also, the object distance (d_0) is 10 cm.

Now, let’s find the image distance (d₁) using the magnification formula:

3 = −d₁/10

Solving for d₁:

d₁= − 30 cm

The negative sign indicates that the image is formed on the same side as the object (in front of the mirror). So, the real and magnified image is located 30cm in front of the concave mirror.