Question

the image of an object is at 8 cm from the convex mirror .if focal length of the mirror is 16 cm.then,determine the object distance​

Answer 1

Given :

Distance of image = 8 cm

Focal length = 16 cm

Type of mirror : convex

To Find :

Distance of object.

Solution :

❖ Focal length of concave mirror is taken negative and that of convex mirror is taken positive.

• Distance of object can be calculated by using mirror formula which is given by

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

• u denotes distance of object
• v denotes distance of image
• f denotes focal length

By substituting the given values;

$\sf:\implies\:\dfrac{1}{u}+\dfrac{1}{v}=\dfrac{1}{f}$

$\sf:\implies\:\dfrac{1}{u}+\dfrac{1}{8}=\dfrac{1}{16}$

$\sf:\implies\:\dfrac{1}{u}=\dfrac{1}{16}-\dfrac{1}{8}$

$\sf:\implies\:\dfrac{1}{u}=\dfrac{1-2}{16}$

$:\implies\:\underline{\boxed{\bf{\gray{u=-16\:cm}}}}$

Answer 2

Question :-

• The image of an object is at 8 cm from the convex mirror .if focal length of the mirror is 16 cm.then,determine the object ddistance.

Given :-

• Distance of Image ( v ) = 8cm
• Focal length ( f ) = 16cm

To Find :-

• Distance of the Object .

Solution :-

Object distance can be calculated as follows :

$\qquad \quad {:} \longrightarrow \sf \boxed{\bf{ \dfrac{1}{u}+\dfrac{1}{v}=\dfrac{1}{f} }}$

• u denotes distance of object
• v denotes distance of image
• f denotes focal length

$\qquad \quad {:} \longrightarrow \sf {\sf{ \dfrac{1}{u}+\dfrac{1}{8}=\dfrac{1}{16} }}$

$\qquad \quad {:} \longrightarrow \sf {\sf{ \dfrac{1}{u}=\dfrac{1}{16} - \dfrac{1}{8}}}$

$\qquad \quad {:} \longrightarrow \sf {\sf{ \dfrac{1}{u}=\dfrac{1 \: \times \: 1 }{16 \: \times \: 1} - \dfrac{1 \: \times \: 2}{8 \: \times \: 2}}}$

$\qquad \quad {:} \longrightarrow \sf {\sf{ \dfrac{1}{u}=\dfrac{1 \: - \: 2 }{16 \: } }}$

$\qquad \quad {:} \longrightarrow \sf {\sf{ \dfrac{1}{u}=\dfrac{ - 1 }{16 \: } }}$

$\qquad \quad {:} \longrightarrow \sf {\bf{ u \: = \: - 16m}}$

━━━━━━━━━━━━━━━━━━━━━━━━━

So, the object distance is -16cm

━━━━━━━━━━━━━━━━━━━━━━━━━