Question

i) A converging mirror form a real image of height 4 cm of an object of height 1 cm placed 20 cm away from the mirror :

a) Calculate the image distance.
b) What is the focal length of the mirror?​

Answer 1

Answer :-

a) Distance of image is 80 cm .

b) Focal length of the mirror is 16 cm .

Explanation :-

We have :-

→ A converging [concave] mirror

→ Height of image = - 4 cm [real image]

→ Height of object = 1 cm

→ Distance of the object = 20 cm

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Since, the mirror is concave :-

• u = -20 cm

From, the formula of magnification :-

m = -(v/u) = hᵢ/hₒ

⇒ -(v/u) = hᵢ/hₒ

⇒ -(v/-20) = -4/1

⇒ v/20 = -4

⇒ v = 20(-4)

⇒ v = -80 cm

[Negative sign of 'v' shows image is formed on the left of the mirror.]

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Now, according to mirror formula :-

1/v + 1/u = 1/f

⇒ 1/(-80) + 1/(-20) = 1/f

⇒ -1/80 + (-1)/20 = 1/f

⇒ (-1 - 4)/80 = 1/f

⇒ -5/80 = 1/f

⇒ -5f = 80

⇒ f = 80/-5

⇒ f = -16 cm

[Focal length of a concave mirror is always negative.]

Answer 2

ANSWER : a) 80cm

                : b) 16cm

Explanation:

IMAGE HEIGHT = 4cm(hi)

OBJECT HEIGHT = 1cm(ho)

OBJECT DISTANCE = 20cm (u)

a) MAGNIFICATION FORMULA = V/U (i)              and      hi/ho(ii)

 EQUATING (i) and (ii)

v/u = hi/ho           v/20=4/1           v=80 cm

b) MIRROR FORMULA = 1/v + 1/u = 1/f

                                      = 1/80 +1/20 =1/f

                                       = 1+4/80 =1/f

                                       = 5/80=1/f

                                       f=80/5      = 16cm