Question

a 10m long awl pin is placed vertically in front of a concave mirror a 5cm long image of the awl pin is formed at 30cm in front of the mirror the focal length of this mirror​

Answer 1

Explanation:

m= h'/h= -v/u

5/10=-30/u

u=-300/5

u=-60cm

1/f=1/v+1/u

1/f = 1/-30 + 1/-60

1/f = -2-1/60

1/f=-3/60

1/f=-1/20

f=-20cm

Therefore the focal length of the concave mirror is 20 cm front of the mirror

Answer 2

Question :-

A 10cm long awl pin is placed vertically in front of a concave mirror a 5cm long image of the awl pin is formed at 30cm in front of the mirror the focal length of this mirror.

Given :-

◉ Height of object, h₁ = + 10 cm

◉ Height of image, h₂ = - 5 cm

◉ Image distance, v = - 30 cm

To Find :-

◉ Focal length of the mirror, f

Solution :-

We know,

⇒ Magnification = - v/u = h₂ / h₁

Where,

• v = Image distance
• u = Object distance
• h₁ = Object height
• h₂ = Image height

⇒ -(-30)/u = -5/10

⇒ 30/u = -1/2

⇒ u = -60 cm

Now,

⇒ 1/f = 1/u + 1/v

⇒ 1/f = -1/60 - 1/30

⇒ 1/f = -1 - 2/60

⇒ 1/f = -1/20

⇒ f = -20 cm

Hence, The focal length of the given concave mirror is -20 cm.

Some Information :-

☛ All measurements measured against the direction of incident ray are taken as negative while measurements taken in the direction of incident ray are taken as positive.

☛ All measurements measured above the principle axis are taken positive while below it are taken negative.