Question

A real image,(⅕)th
the size of the object is formed at a distance of 18 cm from a lens. Then its focal length is :

O f= 16 cm
O f= 17 cm
O f= 13 cm
f= 15 cm​

Answer 1

Answer:

Given: a real image is

5

1

th

the size of the object, and it is formed at a distance of 18cm from the mirror.

To find the focal length of the mirror and the nature of the mirror.

Solution:

According to the given criteria,

image distance, v=−18cm

magnification, m=−

5

1

as the image formed is real hence it will be inverted.

We know,

m=−

u

v

⟹−

5

1

=−(

u

−18

)

⟹u=−(5×18)=−90cm

Applying the lens formula,

f

1

=

v

1

+

u

1

⟹

f

1

=

−18

1

+

−90

1

⟹

f

1

=

90

−5−1

⟹f=−15cm

Since focal length is negative, therefore it is a concave mirror.

Answer 2

Answer:

Given: a real image is 51th the size of the object, and it is formed at a distance of 18cm from the mirror.

To find the focal length of the mirror and the nature of the mirror.

Solution:

According to the given criteria,

image distance, v=−18cm

magnification, m=−51 as the image formed is real hence it will be inverted.

We know, 

m=−uv⟹−51=−(u−18)⟹u=−(5×18)=−90cm

Applying the lens formula,

f1=v1+u1⟹f1=−181+−901⟹f1=90−5−1⟹f=−15cm

Since focal length is negative, therefore it is a concave mirror.

I hope it is helpful to you