Question

For a concave mirror prove that r = 2f​

Answer 1

Answer :

Assuming that a ray of light is coming from infinite distance and strikes on the concave mirror directly. (Ray of light is parallel to the main axis)

• We know that, Any incident ray traveling parallel to the principal axis will pass through the focal point after reflection.

Now see the attachment carefully! :)

❒ Question is totally based on geometry only.

For ∆CMN :

$\sf:\implies\:tan\:i=\dfrac{MN}{CN}$

$\sf:\implies\:MN=tan\:i\cdot CN$

Here angle i is small, Therefore,

• tan i ≈ i

$\sf:\implies\:MN=i\cdot CN\:\dots\:(I)$

For ∆FMN :

$\sf:\implies\:tan\:2i=\dfrac{MN}{FN}$

$\sf:\implies\:MN=tan\:2i\cdot FN$

Applying same condition,

$\sf:\implies\:MN=2i\cdot FN\:\dots\:(II)$

By equating both equations, we get

$\sf:\implies\:i\cdot CN=2i\cdot FN$

$\sf:\implies\:CN=2FN$

• CN = R = Radius of curvature
• FN = f = Focal length

$:\implies\:\underline{\boxed{\bf{\gray{R=2f}}}}$

Answer 2

Answer:

The normal to the surface at point B = R, is the radius of curvature. oncave mirror) or will appear to diverge from (convex mirror) ands law of reflection,

Explanation:

i hope this helps u