A 10 mm Long Awl Pin is Placed Vertically in Front of a Concave Mirror. A 5 mm Long Image of the Awl Pin is Formed at 30 Cm in Front of the Mirror. The Focal Length of This Mirror is?

By K Balaji|Updated : November 7th, 2022

(a) 30 cm

(b) 20 cm

(c) 40 cm

(d) 60 cm

A 10 mm long awl pin is placed vertically in front of a concave mirror. A 5 mm long image of the awl pin is formed at 30 cm in front of the mirror. The focal length of this mirror is 20 cm.

Step 1: Given data

Since the image is real and is formed in front of the mirror,

v = -30 cm

Height of the image hi = 5 mm = 0.5 cm

Height of the object h0 = 10 mm = 1 cm

Step 2: Now we have to calculate the Image Distance

Since the magnification for a concave mirror is specified as,

m = hi/h0 = -v/u

substituting the values in above equation, we get,

0.5/1 = - (-30)/u

On rearranging we get

u = 30/0.5 = 60

Since, the object is in front of the mirror,

u = -60 cm

Step 3: Now we have to Calculate the Focal Length

According to the mirror formula, the focal length is given by

1/f = 1/v + 1/u

Now substituting the values in above equation we get,

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

= -(2 + 1)/ 60

On simplifying we get

= -3/60

= -1/20

f = -20 cm

Focal length cannot be negative so f = 20cm

Summary:-

A 10 mm Long Awl Pin is Placed Vertically in Front of a Concave Mirror. A 5 mm Long Image of the Awl Pin is Formed at 30 Cm in Front of the Mirror. The Focal Length of This Mirror is?

In front of a concave mirror, a vertically positioned 10 mm long awl pin is positioned. At 30 cm in front of the mirror, a 5 mm long picture of the awl pin is created. This mirror's focal length is 20 cm.

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