Question

At what distance from a concave mirror of focal length 10 cm should an object 2 cm long be placed to get an erect image 6 cm tall?​

Answer 1

Given :-

◉ A concave mirror of focal length 10 cm

• An object of height 2 cm
• Height of erect image formed = 6 cm

To Find :-

◉ Distance at which the object should be placed to get an erect image of height 6 cm.

Solution :-

According to the sign convention,

☛ Focal length of a concave mirror is always negative.

☛ Distance of object is always negative.

So, We have

• Focal length, f = -10 cm
• Height of object, h₁ = +2 cm
• Height of image, h₂ = +6 cm

We know,

⇒ Magnification = - v/u = height of image / height of object

⇒ 6 / 2 = -v / u

⇒ 3 = -v / u

⇒ v = - 3u ...(1)

Now, Using the mirror formula, we have

⇒ 1/f = 1/v + 1/u

⇒ -1/10 = -1/3u + 1/u [ from (1) ]

⇒ -1/10 = 1/u - 1/3u

⇒ -1/10 = (3 - 1)/3u

⇒ -1/10 = 2/3u

⇒ 3u = -20

⇒ u = -20/3 cm or -6.67 cm

Therefore, The object should be placed at a distance of 6.67 cm infront of the mirror.