Question

A converging mirror forms a real image of height 4cm of an object of height 1cm placed 20cm away the mirror . calculate the image distance and what is the focal length of the mirror​

Answer 1

Answer:

Here, height of image, `h_(2) = -4 cm`, minus sign is for real image, which is inverted i.e. below the principal axis.

Height of object, `h_(1) = + 1 cm`.

Object distance, `u = -20 cm`, minus sign for the object distance is measured from pole in a direction opposite to the direction of incidence of light.

We have to calculate the image distance, `v = ?`

As `m = h_(2)/h_(1) = -v/u`,

putting the values given above, we get `(-4)/1 = (-v)/(-20)` or `v = -80 cm`

Negative sign of v indicates that the image is on the side of the object. It must be real and inverted.

To calculate focal length of the mirror, we use mirror formula :`(1)/(f) = (1)/(u) + (1)/(v)`

putting `u = -20 cm`, and `v = - 80 cm`, `(1)/(f)=(1)/(-20)+(1)/(-80) = (-4-1)/(80) = (-5)/(80)`

`f = (-80)/5 = -16cm`

Negative sign of f indicates that mirror is concave.