Rajashree wants to get an inverted image of height 5 cm of an object kept at a distance of 30 cm from a concave mirror. The focal length of the mirror is 10 cm. At what distance from the mirror should she place the screen ? What will be the type of the image, and what is the height of the object?

Here it says that the focal length = f = -10cm, while the object distance(u) = – 30cm and height of the image (h₂) =- 5 cm. Hence, we need to find image distance(v)= ? and height of the object(h₁) = ?

Now, to get the image distance or v, you can apply the mirror formula here. That is,

1/v + 1/u = 1/f

1/v= (1/f) – (1/u)

1/ v = (1/ -10) – (1/ -30)

Hence, 1 / v = (- 3 + 1) / 30 = -2 / 30

1/ v = – 1 /15cm

v=-15cm

From this we can deduce that Rajashree has to keep the screen 15 cm to the left of the mirror.

Then to calculate the height of the object, you can use the magnification expression.

That is, M = h₂ / h₁= – (v/u)

Hence, h₁ = – (uh₂ / v)= – (-30) (-5) / -15

Therefore, h₁ = ( -2) (-5) = 10 cm

So, the height of the object is 10cm. Thus, the image will be real and diminished.