Question

Find the distance of image when an object is placed at a distance of 10 cm infront of concave mirror whose focal length is 4cm

Answer 1

GIVEN :-

• Distance of object (u) = 10 cm.
• Focal Length (f) = 4 cm.

TO FIND :-

• The distance of image (v)

SOLUTION :-

➠ Since the mirror is concave so there distance of object and focal length will be negative.

➠ Let's applied the mirror formula.

$\dag \boxed{ \red{ \bf \: \dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v} }}$

➠ Now substitute all the values,

$\to \rm \: \dfrac{1}{-4} = \dfrac{1}{-10} + \dfrac{1}{v} \\ \\ \to \rm \: \dfrac{1}{v} = \dfrac{1}{-4} - \dfrac{1}{-10} \\ \\ \to \rm \: \dfrac{1}{v} = \dfrac{1 \times 5}{-4\times 5} - \dfrac{1 \times 2}{-10 \times 2} \\ \\ \to \rm \: \dfrac{1}{v} = \dfrac{5 - 2}{-20} \\ \\ \to \rm \: \dfrac{1}{v} = \dfrac{3}{-20} \\ \\ \to \boxed{\red{\rm v = \dfrac{-20}{3} }}$

Hence the distance of image is -20/3 cm.

ADDITIONAL INFORMATION :-

➠ Focal Length :- The distance between the pole and the focus of the mirror is termed as focal length .

➠ Centre of curvature :- The centre of curvature of a spherical mirror is the centre of the sphere.

➠ Principal Axis :- The line joining of pole and the mirror and its centre of curvature is called principal axis .

Answer 2

$\bf{\underline{Question :-}}$

• Find the distance of image when an object is placed at a distance of 10 cm infront of concave mirror whose focal length is 4cm

$\bf{\underline{Given :-}}$

● Distance of object (u) = 10 cm.

● Focal Length (f) = 4 cm.

$\bf{\underline{To \:Find :-}}$

● The distance of image (v) =?

WE KNOW,

$\bf{\underline{\red{\fbox{MIRROR\:FORMULA :-}}}}$

$\huge ★ \bf{\purple {\frac{1}{f} = \frac{1}{u} + \frac{1}{v}}}$

$\bf{\underline{Solution :-}}$

$\sf → \huge \frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

$\sf → \huge \frac{1}{4} = \frac{1}{10} + \frac{1}{v}$

$\sf → \huge \frac{1}{v} = \frac{1}{4} - \frac{1}{10}$

• (Taking L.C.M of 4 and 10 is = 20 )

$\sf → \huge \frac{1}{v} = \frac{ 5 - 2}{20}$

$\sf → \huge \frac{1}{v} = \frac{3}{20}$

$\bf{\underline{Hence :-}}$

• Distance of image is = 3/20 cm