Question

8.) What is the distance of a needle from a concave mirror of focal length 10 cm for which a virtual
image of twice its height of formed ?
A) 2.5 cm
B) 5 cm
C) 8 cm
D) 9.1 cm​

Answer 1

Answer:

Given: Focal length of Mirror = 10 cm

           Height of Virtual Image formed(hₐ) = 2 × Height of Object(hₓ)

To Find: Distance of needle/object(u).

Now, we are given focal length of concave mirror to be 10 cm. The ratio of height of image to height of object is 2.

Hence,

Height of image ÷ Height of object = 2

Now, this relation is known as Magnification of Image in Optics, denoted by M.

Hence, M = 2

Another formula for magnification of mirror is -v/u, where, v = distance of image from mirror and u = distance of object from mirror.

Therefore, M = 2 = -v/u

This gives v = -2u.

Now, from the mirror formula for concave mirror, we get :

1/f = 1/u + 1/v

Putting value of v = -2u and f = -10(according to sign convention).

-1/10 = 1/u + 1/(-2u)

-1/10 = 1/u - 1/2u

-1/10 = (1/u)(1-1/2)

-1/10 = (1/u)(1/2)

-2/10 = 1/u

-1/u = 1/5

u = -5 cm.

Therefore, the distance of object from mirror is, u = 5 cm.

Hence, B) 5 cm is the correct option.

Answer 2

Answer:

correct option B)

The distance of the object from mirror is u = 5cm.

Explanation:

Given:

•  Focal length of Mirror = 10 cm

•  Height of Virtual Image formed(hₐ) = 2 × Height of Object(hₓ)

  To Find:

•  Distance of needle/object(u).    

solution:

•  Now, we are given focal length of concave mirror to be 10 cm. The ratio of height of image to height of object is 2.
• hence,  
• Height of image ÷ Height of object = 2

Now, this relation is known as Magnification of Image in Optics, denoted by M.

Hence, M = 2

Another formula for magnification of mirror is -v/u, where, v = distance of image from mirror and u = distance of object from mirror.

• Therefore, M = 2 = -v/u

• This gives v = -2u.

Now, from the mirror formula for concave mirror, we get :

• 1/f = 1/u + 1/v

Putting value of v = -2u and f = -10(according to sign convention).

• -1/10 = 1/u + 1/(-2u)
• -1/10 = 1/u - 1/2u
• -1/10 = (1/u)(1-1/2)
• -1/10 = (1/u)(1/2)
• -2/10 = 1/u
• -1/u = 1/5
• u = -5 cm.

Therefore, the distance of object from mirror is, u = 5 cm.

Hence, B) 5 cm is the correct option.