Question

Draw diagrams for concave mirrors of radii 5cm, 7cm and 10cm with common centre of
curvature. Calculate the focal length for each mirror. Draw a ray parallel to the common
principal axis and draw reflected rays for each mirror.

Answer 1

Diagram for concave mirrors:

• We know that for paraxial rays, the focal length of any spherical mirror is half of the radius of curvature of the mirror.

So, the focal lengths of the mirrors will be :

• f1 = C_(1)/2 = 5/2 = 2.5 cm
• f2 = C_(2)/2 = 7/2 = 3.5 cm
• f3 = C_(3)/2 = 10/2 = 5 cm

Here "f" represents focal length and "C" represents Radii of curvature

Now, we know that paraxial light rays after reflection from a concave mirror will pàss through the focus of the mirror.

$\star$ Refer to attached diagram.

Answer 2

$\huge{ \bold{ \underline{ \underline{Explanation}}}}$

A beam of light incident on a spherical mirror parallel to the principal axis converges focus perpendicular to the principal axis is called the focal plane.

to or appears to diverge from a common point after reflection. This point is known as principal focus of the mirror. The distance between the pole and the

principal focus gives the focal length of the mirror. A plane passing through the focus perpendicular to the principal axis is called the focal plane.

$\: \: \: \: \sf{ R = 5 \: cm } \\ \\ \bold{f = \frac{R}{2} } \\ \\ \: \sf{f = \frac{5}{2} }$

$\bold{f = 2.5 \: cm}$

$\sf{R = 7 \: cm} \\ \\ f = \frac{R}{2} \\ \\ \sf{f = \frac{7}{2} }$

$\red{\bold{f = 3.5 \: cm}}$

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