Question

A converging beam of light rats falls on a concave mirrir of focal length 20 cm. They appear to meet at a point which is 30 cm away from pole and 10 cm below principal axis. Find the location and nature of image formed​

Answer 1

Explanation:

Given:-

• Focal Length ,f = -20cm
• Image distance ,v = -30cm
• Image height ,hi = -10 cm (below the principal axis.)

To Find:-

• Location & Nature of Image Formed

Solution:-

As it is given that the mirror is converging mirror . When light rays fall on the mirror its forms an image 30 cm away from the pole. And also the image formed by concave mirror is real & Inverted .

Firstly, we calculate the image distance

Using Mirror Formula

• 1/v + 1/u = 1/f

Substitute the value we get

→ -1/30 + 1/u = 1/(-20)

→ -1/30 + 1/u = -1/20

→ 1/u = -1/20 + 1/30

→ 1/u = -3+2/60

→ 1/u = -1/60

→ u = -60 cm

• Hence, the object distance is 60 cm in front of mirror.

Now, Calculating the Magnification

• m = hi/ho = -v/u

Substitute the value we get

→ -10/ho = -(-30)/-60

→ -10/ho = -30/60

→ -10/ho = -1/2

→ ho = 20 cm

• Hence, the height of the object is 20 cm.
• Nature of Image :- Real & Inverted .

Answer 2

Answer:

Given :-

• Focal length = -20 cm
• Image Distance = -30 cm
• Image height = -10 cm

To Find :-

• Location
• Nature

Solution :-

According to mirror formula

$\sf \: \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$

V = Image Distance

U = Object Distance

F = Focal length

1/-30 + 1/u = 1/-20

-1/30 + 1/u = -1/20

1/u = -1/20 - -1/30

1/u = -1/20 + 1/30

1/u = -3 + 2/60

1/u = -1/60

u = 60 × -1

u = -60 cm

Now,

Magnification

$\sf \dfrac{hi}{ho} = \dfrac{ - v}{u}$

-10/ho = -30/60

-10/ho = -3/6

-10/ho = -1/2

ho = 2 × 10

ho = 20 cm

Conclusion :-

• Object Distance = -60 cm
• Object Height = 20 cm
• Nature = Real and Inverted