List the sign conventions for reflection flight by spherical mirr… - Vidyadip

Question

List the sign conventions for reflection flight by spherical mirrors. Draw a diagram and apply these conventions in the determination of focal length of spherical mirror which forms a three times magnified real image of an object placed 16 cm infront of it.

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Answer

Sign conventions for reflection of light by spherical mirror are:

The object is always placed to the left of the mirror.
All the distances parallel to the principal axis are always measured from the pole of the spherical mirror.
All the distances measured along the direction of incident light (along +ve x-axis), are considered to be positive.
Those distances measured opposite to the direction of incidence light (i.e. along -ve x-axis), are taken as negative.
The distances measured in upward direction, i.e. perpendicular to and above the principal axis (along +ve y-axis), are taken as positive.
The distances measured in the downward direction, (along -ve y-axis), i.e. perpendicular to and below the principal axis are taken as negative.

From the question

u = -16cm, m = -3 for real

But $\text{m}=-\frac{\text{v}}{\text{u}}=-3$

$\Rightarrow\text{v}=3\text{u}=3(-16)=-48\text{cm}.$

Using mirror fornula

$\frac{1}{\text{f}}=\frac{1}{\text{v}}+\frac{1}{\text{u}}$

We get, $=\frac{1}{\text{f}}=\frac{1}{-48}+\frac{1}{-16}$

$=\frac{1}{-48}+\frac{1}{-16}=\frac{-1-3}{48}=\frac{-4}{48}=\frac{-1}{12}$

$\text{f}=-12\text{cm}$

So, focal lenght of spherical mirror is 12cm. Negative sign of focal length indicates that mirror is concave in nature.

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