Question

three times magnified real image of an object is formed by a concave mirror when the object placed 20 cm from it. Where is the image formed?Also calculate the focal length of the given mirror
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Answer 1

AnswEr :

Real magnified image is formed and focal length of the given mirror is 15 cm .

Step-by-step explanation :

GivEn :

• Distance of the object (u) = -20 cm [sign convention]

• Magnification = -3

To find :

• To calculate the focal length and the image formed = ?

SoluTion :

Firstly we'll calculate the focal length so that we'll come to know that where is the image formed.

For calculating, the focal length we've to find the distance of the image first.

As the magnification is given,

Applying magnification formula,

$: \implies \sf \: \: m = \dfrac{ - v}{u}$

$: \implies \sf \: \: - 3 = \dfrac{ - v}{ - 20}$

$: \implies \sf \: \: - v = - 20 \times - 3$

$: \implies \sf \: \: - v = 60$

$: \implies \textbf { \textsf { v = - 60 }}$

Hence, distance of the object is -60 cm .

Now,

Using the mirror formula,

$: \implies \sf \: \: \dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$

$: \implies \sf \: \: \dfrac{1}{f} = \dfrac{1}{ - 60} + \dfrac{1}{ - 20}$

$: \implies \sf \: \: \dfrac{1}{f} = - \dfrac{1}{ 60} - \dfrac{1}{ 20}$

$: \implies \sf \: \: \dfrac{1}{f} = - \dfrac{1}{ 60} - \dfrac{1 \times 3}{ 20 \times 3}$

$: \implies \sf \: \: \dfrac{1}{f} = - \dfrac{1}{ 60} - \dfrac{ 3}{60}$

$: \implies \sf \: \: \dfrac{1}{f} = \dfrac{ - 4}{60}$

$: \implies \sf \: \: \dfrac{1}{f} = \dfrac{ - 1}{15}$

$: \implies \: \: \textsf{ \textbf{f = - 15 \: cm}}$

Therefore, focal length of the mirror is 15 cm.

Thus, we can conclude that a concave mirror forms a real magnified image only when the image to be formed is inverted as m= -3

Answer 2

Answer:

v = - 60 cm

f = - 15 cm

Explanation:

Since it a real image, magnification will be negative

m = -3

u = -20cm

v = ?

By magnification formula

m = -v/u

-3 = -v / - 20

-3×20=v

-60 (cm) = v

By mirror formula

1/f = 1/v + 1/u

1/f = 1/-60+(1/-20)

1/f = -1-3/60

1/f = -4/60

1/f = -1/15

f = - 15 (cm)