Question

A body of length 6cm is placed 10cm from a concave mirror of focal length 20cm.Find the position,size and nature of the image

Answer 1

Explanation:

Given:-

• Object height ,hi = 6 cm

• Object Distance ,u = -10 cm

• Focal length ,f = -20 cm

To Find:-

• The position,size and nature of the image.

Solution:-

Firstly we calculate the image position . Using Mirror Formula

• 1/v + 1/u = 1/f

Substitute the value we get

→ 1/v = 1/f - 1/u

→ 1/v = 1/(-20) - 1/(-10)

→ 1/v = -1/20 + 1/10

→ 1/v = -1+2/20

→ 1/v = 1/20

→ v = 20 cm

• Positive sign show that the image formed is virtual & erect.
• Position of Object = between Pole & Focus.

Now, calculating the height of image. Using Magnification Formula

• m = hi/ho = -v/u

Substitute the value we get

→ hi/6 = -20/-10

→ hi/6 = 2

→ hi = 12 cm

• Hence, the height of the image is 12 cm .

Answer 2

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• 1/v + 1/u = 1/f

Substitute the value we get

- 1/v = 1/f - 1/u

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

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

1/v = -1+2/20

1/v = 1/20

+ v = 20 cm

• Positive sign show that the image formed is virtual & erect. • Position of Object = between Pole & Focus.

Now, calculating the height of image. Using Magnification Formula

m = hi/ho = -v/u

Substitute the value we get

- hi/6 = -20/-10

- hi/6 = 2

- hi = 12 cm

• Hence, the height of the image is 12 cm.

$\Huge \boxed{ \colorbox{cyan}{hope \: this \: helps}}$