Question

candle flame 1.6 cm high is imaged in a ball bearing of diameter 0.4 M the ball bearing is 20 CM away from the flame find the location and the height of the image hC verma​

Answer 1

Given that,

Height of image taken as object (ho) = 1.6 cm

Diameter of ball bearing (D) = 0.4 cm

Radius (R) = Diamter/2 = 0.4/2 = 0.2 cm

Image distance from mirror (u) = -20 cm

We have to find the location and the height of the image.

Now,

Mirror Formula:

1/f = 1/v + 1/u

2/R = 1/v + 1/u

→ 2/0.2 = 1/v + 1/(-20)

→ 1/0.1 = 1/v - 1/20

→ 10 + 1/20 = 1/v

→ (200 + 1)/20 = 1/v

→ 201/20 = 1/v

→ v = 20/201 = 0.1 cm

Now,

m = hi/ho = -v/u

→ hi/1.6 = -0.1/-20

→ hi/1.6 = 1/200

→ hi = 1.6/200

→ hi = 0.008 cm

Therefore,

The distance of the image (v) is 0.1 cm and the height of the image (hi) = 0.008 cm.

Answer 2

Explanation:

Given -

ho = 1.6 cm

Diameter of ball bearing = 0.4 cm

Object distance from mirror = - 20 cm

To Find -

Location and height of the image

Now,

As we know that,

• Mirror formula = 1/f = 1/v + 1/u

here,

f = focal length of mirror

v = image distance from mirror

u = object distance from mirror

Now,

= 2/R = 1/v + 1/u

here,

R = 0.2 cm, because

radius = diameter/2 = 0.4/2 = 0.2cm

= 2/0.2 = 1/v + 1/u

= 10 = 1/v + 1/(-20)

= 10 = 1/v - 1/20

= 10 + 1/20 = 1/v

= 200 + 1/20 = 1/v

= 201/20 = 1/v

= v = 20/201

• = v = 0.1 cm (approx)

Now,

• m = hi/ho = -v/u

here,

m = magnification

hi = height of image

ho = height of object

Now,

= hi/1.6 = (-0.1)/(-20)

= hi = 1.6 × 0.1/20

= hi = 16/2000

= hi = 0.008 cm

Hence,

Distance of image is 0.1 cm

and

height of image is 0.008 cm