Question

an object is placed at a distance of 30 cm from a concave mirror of focal length 20cm. where will the image be formed.

Answer 1

u=30 cm

f=20 cm

v=?

mirror formula

1/f=1/v+1/u

for concave mirror f is in -ve

1/-20=1/v-1/30

1/v=-1/20+1/30

1/v=-3+2/60

1/v=-1/60

v=-60 cm

hence image is formed at 60 cm at the same side of the mirror as that of the object

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Answer 2

Given:

• Object distance = 30 cm
• Focal length of mirror = 20 cm.
• Mirror is concave

To find:

• Image distance ?

Calculation:

Applying the MIRROR FORMULA:

$\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$

$\implies \dfrac{1}{( - 20)} = \dfrac{1}{v} + \dfrac{1}{( - 30)}$

$\implies - \dfrac{1}{ 20} = \dfrac{1}{v} - \dfrac{1}{30}$

$\implies \dfrac{1}{v} = - \dfrac{1}{20} + \dfrac{1}{30}$

$\implies \dfrac{1}{v} = \dfrac{ - 3 + 2}{60}$

$\implies \dfrac{1}{v} = \dfrac{ - 1}{60}$

$\implies v = - 60 \: cm$

So, image is produced 60 cm in front of the mirror.