Question

5 (1) Define power and it's Sl unit of a lens? Find the power of a concave lens of focal length 2m
(11) Size of image of an object by a mirror having a focal length of 20 cm is observed to be
reduced to 1/3rd of its size. At what distance the chinath​

Answer 1

Answer:

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(QI)Define power and it's Sl unit of a lens? Find the power of a concave lens of focal length 2m

(A) Definition: The power of a lens is defined as the inverse of the focal length (in meters) of the lens. It is a measure of the amount of deviation of light ray produced by a lens, the more the power, the more is the deviation.

SI unit : Unit of power is Dioptre (D).

The power of the lens P= 1/f

Focal length of concave lens f= -2m  

P= 1/-2

Then the power of the lens P= -0.5 dioptre  

The diopter is the unit of measure for the refractive power of a lens. The power of a lens is defined as the reciprocal of its focal length in meters or P= 1/f where P is the power in dioptres and f is the focal length in meters.

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(QII)The size of the image of an object by a mirror having a focal length of 20cm is observed to be reduced to 1/3rd of its size. At what distance the object has been placed from the mirror? What is the nature and size?

(A) As we know, m = - v/u = h₁/h₂

⇒ - v/u = 1/3 h₂/h₂

⇒ u = - 3v

Applying mirror formula,

1/v + 1/u = 1/f, we get

when f = + 20 cm

⇒ 1/v - 1/3v = 1/20

⇒ 3 - 1/3v = 1/20

⇒ 2/3v = 1/20

⇒ 3v = 2 × 20

⇒ v = 2 × 30/3

⇒ v = 40/3 .. (i)

u = - 3v

By putting v value, we get

⇒ u = - 3 × 40/3

⇒ u = - 40 cm.

Object Distance = - 40 cm  

If we take f = - 20 cm, the value of u will be + 40 cm which is not possible.  

m = - v/v

⇒ m = - 40/3/- 40  

⇒ m = + 1/3  

⇒ m = 0.33 cm  

This implies that the nature of the image is erect and diminished.

Nature of Image = Convex Mirror.

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