A converging mirror forms a real image of height 4 cm, of an object of height 1 cm placed 20 cm away from the mirror. Calculate the image distance. What is the focal length of the mirror ?

Options

A. -80 cm , -16 cm
B. 80 cm , 16 cm
C. -60 cm , -12 cm
D. NONE

Answer

A

Explanation

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.