Question

61. An object placed 20 cm in front of a mirror is found to have an image 15 cm (a) in front of it, (b)
behind it. Find the focal length of the mirror and the kind of mirror in each case.

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Answer 1

Answer:

Explanation:

hello

CASE A

with sign convention

u= -20

v= -15

using mirror formula

1/v+1/u=1/f

-1/15-1/20 =1/f

-4-3/60=1/f

f= -60/7

since f is negative, therefore it is a concave mirror.

CASE B

U= -20

v= +15

using mirror formula

1/v+1/u= 1/ f

1/15-1/20=1/f

4-3/60=1/f

f=60

f is positive so it is a convex mirror..........

Answer 2

Answer:

The focal length for concave and convex  mirror is 8.57 cm and 60 cm.

Explanation:

Given that,

Distance of the object u = -20 cm

Distance of the image v = 15 cm

Using mirror's formula

$\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}$

Where, f = focal length

u = distance of the object from the mirror

v = distance of the image from the mirror

If the image is formed in front of the mirror

So, v = -15 cm

Then the focal length is

$\dfrac{1}{f}=\dfrac{1}{-20}+\dfrac{1}{-15}$

$\dfrac{1}{f}=\dfrac{1}{-20}-\dfrac{1}{15}$

$\dfrac{1}{f}=-\dfrac{7}{60}$

$f =-\dfrac{60}{7}$

$f = -8.57\ cm$

The focal length is negative.

Therefore, it is a concave mirror.

If the image is formed behind the mirror

So, v = 15 cm

Then the focal length is

$\dfrac{1}{f}=\dfrac{1}{-20}+\dfrac{1}{-15}$

$\dfrac{1}{f}=\dfrac{1}{-20}+\dfrac{1}{15}$

$\dfrac{1}{f}=\dfrac{1}{60}$

$f =60$

The focal length is positive.

Therefore, it is a convex mirror.

Hence, The focal length for concave and convex  mirror is 8.57 cm and 60 cm.