Question

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

Answer 1

Given:-

Size of pin, h = 10 mm = 1 cm

Size of image formed of pin, h' = 5 mm = 0.5 cm

Image distance from the mirror of pin, in front of mirror, v = - 30 cm

To find:-

Focal length of the mirror?

Solution:-

☯ Let f be the focal length of mirror.

We know that,

h'/h = - v/u [ from formula to find magnification ]

⇒ u = - vh/h'

⇒ u = (- 30 × 1)/0.5

⇒ u = (- 30 × 10)/ 5

⇒ u = - 300/5

⇒ u = - 60 cm

∴ Object distance, u is - 60 cm

★ Now, Using mirror formula,

1/f = 1/v + 1/u

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

1/f = 1/20

f = - 20 cm

∴ Hence, Focal length of mirror is 20 cm.

Answer 2

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

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Given:-

Size of pin, h = 10 mm = 1 cm

Size of image formed of pin, h' = 5 mm = 0.5 cm

Image distance from the mirror of pin, in front of mirror, v = - 30 cm

To find:-

Focal length of the mirror?

Solution:-

☯ Let f be the focal length of mirror.

We know that,

h'/h = - v/u [ from formula to find magnification ]

⇒ u = - vh/h'

⇒ u = (- 30 × 1)/0.5

⇒ u = (- 30 × 10)/ 5

⇒ u = - 300/5

⇒ u = - 60 cm

∴ Object distance, u is - 60 cm

★ Now, Using mirror formula,

1/f = 1/v + 1/u

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

1/f = 1/20

f = - 20 cm

∴ Hence, Focal length of mirror is 20 cm.

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