Question

an object is placed 20 cm in front of a mirror find its focal length if
(a)15 cm in front of the mirror​

Answer 1

Answer:

Step-by-step explanation:

CASE A:

            With sign convention  

                      u = -20  , v = -15

Using mirror formula;

                        1/v + 1/u = 1/f

                     -1/15 - 1/20 = 1/f

                    - 4 - 3 / 60 = 1/f

                       f = - 60 / 7

Since;  f is negative, therefore, it is a concave mirror.

CASE B:

                U = - 20 v = + 15

Using mirror formula

                1/v + 1/u = 1/ f

               1/15 - 1/20 = 1/f

                  4 - 3 / 60 = 1/f

                         f = 60

f is positive so it is a convex mirror

Answer 2

Answer:

✯If the mirror is convex

➩ The distance of object ( u) = -20 cm

➩ Front of mirror ( v) = -15 cm

✯Formula,

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

Substitute the values in formula,

$: { \implies{ \sf{ \frac{1}{f} = \frac{1}{ - 15} + \frac{1}{ - 20} }}}$

$\: : { \implies{ \sf{ \frac{1}{f} = \frac{1}{ - 15} - \frac{1}{20} }}}$

$\: \: : { \implies{ \sf{ \frac{1}{f} = \frac{ - 4 - 3}{60} }}}$

$\: \: : { \implies{ \sf{ \frac{1}{f} = \frac{ - 7}{60} }}}$

$\: \: \: : { \implies{ \sf{ f = \frac{ - 60}{7} }}}$

✯If the mirror is concave

➩ The distance of object ( u) = - 20 cm

➩ Front of mirror ( v) = 15 cm

✯Formula,

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

Substitute the values in formula,

$: { \implies{ \sf{ \frac{1}{f} = \frac{1}{ 15} + \frac{1}{ - 20} }}}$

$\: : { \implies{ \sf{ \frac{1}{f} = \frac{1}{ 15} - \frac{1}{20} }}}$

$\: \: : { \implies{ \sf{ \frac{1}{f} = \frac{ 4 - 3}{60} }}}$

$\: \: : { \implies{ \sf{ \frac{1}{f} = \frac{ 1}{60} }}}$

$:{ \implies{ \sf{f = 60}}}$

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