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Light – Reflection and Refraction — Science STD 10 — Question

CBSE BoardEnglish MediumSTD 10ScienceLight – Reflection and Refraction5 Marks
Question
List the new Cartesian sign convention for reflection of light by spherical mirrors. Draw a diagram and apply these conventions for calculating the focal length and nature of a spherical mirror which forms $\frac{1}{3}$ times magnified virtual image of an object placed 18cm if front of it.
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Answer

New Cartesian Sign Conventions for reflection of light by spherical mirrors are given
below:

  1. The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.
  2. All distances parallel to the principal axis are measured from the pole of the mirror.
  3. All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along - x-axis) are taken as negative.
  4. Distances measured perpendicular to and above the principal axis (along + y-axis) are taken as positive.
  5. Distances measured perpendicular to and below the principal axis (along - y-axis) are taken as negative.

$\text{m}=\frac{1}{3}$

$\Rightarrow\text{u}=-18\text{cm}$

$\Rightarrow\text{f}=?$

$\Rightarrow\text{v}=?$

$\Rightarrow\text{m}=-\frac{\text{v}}{\text{u}}=\frac{1}{3}$

$\Rightarrow\text{v}=-\frac{\text{u}}{3}=-\frac{(-18)}{3}=-6\text{cm.}$

Now, according to mirror formula.

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

$\Rightarrow\frac{1}{6}+\frac{1}{(-18)}=\frac{1}{\text{f}}$

$\Rightarrow\frac{1}{\text{f}}=\frac{3-1}{18}$

$\Rightarrow\frac{1}{\text{f}}=\frac{2}{18}$

$\text{f}=9\text{cm}$

Since, the focal length is positive so, it is a convex mirror.

Ray diagram:


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