Question

an object is placed at
a distance of 4
centimeters in front of a concave mirror
whose focal length is 5 centimeters, where
Is the image formed ?​

Answer 1

Concave mirror :

Object distance(u) = - 4cm.

Focal length (f) = - 5cm.

Image distance(v) = ?

From the mirror formula ,

1/f = 1/v + 1/u.

1/-5 = 1/v + 1/-4.

-1/5 = 1/v - 1/4.

1/v = -1/5 + 1/4.

{Transposing}

1/v = (-4 + 5)/20.

{ LCM is 20 }

1/v = 1/20.

Therefore , v = 20cm .

So, the image is formed at 20cm on the other side of the mirror.

________________

Answer 2

★Solution :-

As per the given data ,

• object distance = - 4 cm

object distance is negative as distances are always measured from the pole of the mirror

• focal length = - 5 cm

focal length of a concave mirror is always negative

As per the mirror formula ,

$\bigstar\boxed{\mathtt{\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}}}$

here ,

• f = focal length
• v = image distance
• u = object distance

$\longrightarrow\mathtt{\dfrac{1}{-5} = \dfrac{1}{v} + \dfrac{1}{-4}}$

$\longrightarrow\mathtt{\dfrac{1}{-5} = \dfrac{1}{v} - \dfrac{1}{4}}$

$\longrightarrow\mathtt{ \dfrac{1}{v}= \dfrac{-1}{5} + \dfrac{1}{4} }$

$\longrightarrow\mathtt{ \dfrac{1}{v}= \dfrac{-4+5}{20} }$

$\longrightarrow\mathtt{ \dfrac{1}{v}= \dfrac{1}{20} }$

$\longrightarrow\mathtt{ v = 20 \: cm }$

The image is formed at a distance of 20 cm from the mirror