Question

Hey guys❤

Tell me about the relationship between the radius of curvature and focal length. ​

Answer 1

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Answer:

f = R/2

Explanation:

✨Firstly Consider the attachment..

$\large\boxed{\fcolorbox{blue}{white}{In\: Attachment}}$

⭕A ray parallel to principal axis after reflection passes through the focus...

⚫Now a ray AB parallel to principal axis falling on a concave mirror at B. After reflection, the ray passes through the focus.

⚫The dotted line CB is the Normal at point B. Therefore, ∠ABC is the angle of incidence i and ∠FBC is the angle of reflection.

∠ABC = ∠FBC _______[law of reflection]

Also, ∠ABC = ∠FCB ______[Alt. int. angles]

therefore, ∠FBC = ∠FCB => FC = FB

⚫Now, if the aperture of the concave mirror is small, then the ray AB will be very close to the principal axis and point B will be very close to P.

Therefore, FB will be approximately equal to FP.

i.e., FC = FP

Now, FP + FC = R ......... [where R = radius of curvature]

therefore, FP + FP = R

=> 2FP = R

=> FP = R/2

=> f = R/2

↑↑↑↑↑↑↑↑↑↑____________PROVED

Answer 2

Before arriving at the answer let us first understand the meaning of these terms:-

⭕RADIUS OF CURVATURE:-

✍It is known to us that a spherical mirror has a pole and a point called the "centre of curvature ".

✍This distance between the pole and the centre of curvature is the RADIUS OF CURVATURE.

⭕FOCAL LENGTH:-

✍It is the length between the pole of a spherical mirror (optical centre of lens) and the focal point.

✍It is positive in case of a convex mirror and negative in that of a concave mirror.

▶️Let us now come at the relation between the focal length and centre of curvature.

$focal \: length = \frac{1}{2} (radius \: of \: curvature)$

⭕One important thing to be noted is that, in case of a plane mirror, the radius of curvature is taken as infinity.

⭕In case of lens ,if you are provided with refractive indices of the medium, you can have the lens maker formula.

$\frac{1}{f} = {n - 1} ( \frac{1}{r1} - \frac{1}{r2} )$

where f is the focal length and r1 and r2 are the radius of curvature respectively. ✔✔