Question

A convex mirror produces magnification
of 1/4 if the focal length of the mirror is
16 cm find position of the object
of image​

Answer 1

Solution :-

◘ Focal length (f) = +16 cm

◘ Magnification, m = 1/4

We know that, for a convex mirror,

$\tt{m=-\dfrac{v}{u} }$

Solving it further :-

$\tt{\dfrac{1}{4}=-\dfrac{v}{u} }\\\\\tt{\hookrightarrow u=-4v}$               .............(1)

Applying mirror formula :-

$\displaystyle{\tt{\frac{1}{v}+\frac{1}{u}=\frac{1}{f} }}\\\\\displaystyle{\tt{\hookrightarrow \frac{1}{v}+\frac{1}{-4v}=\frac{1}{16} }}\\\\\displaystyle{\tt{\hookrightarrow \frac{1}{v}-\frac{1}{4v}=\frac{1}{16} }}\\\\\displaystyle{\tt{\hookrightarrow \frac{4-1}{4v}=\frac{1}{16} }}\\\\\displaystyle{\tt{\hookrightarrow \frac{3}{4v}=\frac{1}{16} }}\\\\\displaystyle{\tt{\hookrightarrow 48=4v}}\\\\\boxed{\boxed{\displaystyle{\tt{\hookrightarrow v=12\ cm}}}}$

Hence, the image distance is 12 cm.

Now, putting the value of v is equation (1) :-

$\tt{u=-4(12)}\\\\\boxed{\boxed{\displaystyle{\tt{\hookrightarrow u=-48\ cm}}}}$

Hence, the object distance is -48 cm.

Answer 2

$\large\underline\bold{ANSWER \red{\huge{\checkmark}}}$

• Focal length (f) = +16 cm
• Magnification, m = 1/4

We know that, for a convex mirror,

$\tt{m=-\dfrac{v}{u} }$

Solving it further :-

$\tt{\dfrac{1}{4}=-\dfrac{v}{u} }\\\\\tt{\hookrightarrow u=-4v}$               .............(1)

Applying mirror formula :-

$\displaystyle{\tt{\frac{1}{v}+\frac{1}{u}=\frac{1}{f} }}\\\\\displaystyle{\tt{\hookrightarrow \frac{1}{v}+\frac{1}{-4v}=\frac{1}{16} }}\\\\\displaystyle{\tt{\hookrightarrow \frac{1}{v}-\frac{1}{4v}=\frac{1}{16} }}\\\\\displaystyle{\tt{\hookrightarrow \frac{4-1}{4v}=\frac{1}{16} }}\\\\\displaystyle{\tt{\hookrightarrow \frac{3}{4v}=\frac{1}{16} }}\\\\\displaystyle{\tt{\hookrightarrow 48=4v}}\\\\\boxed{\boxed{\displaystyle{\tt{\hookrightarrow v=12\ cm}}}}$

Hence, the image distance is 12 cm.

Now, putting the value of v is equation (1) :-

$\tt{u=-4(12)}\\\\\boxed{\boxed{\displaystyle{\tt{\hookrightarrow u=-48\ cm}}}}$

Hence, the object distance is -48 cm.