The relation between Focal length and radius of curvature for spherical mirrors is:

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R = 2f

R =

\frac{f}{2}

R = f

None of these

answer is A.

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Detailed Solution

Concept- The focal length and radius of curvature are inextricably linked. A mirror's focal length and radius of curvature share the same unit. We must also apply the norms or laws of reflection here.
To discover the relationship between focal length and radius of curvature in a spherical mirror.
Think about a concave mirror.
Question Image

Where,

Pole, it is the midpoint of mirror

Focal point

centre of curvature

Radius of creature
Ray parallel to principal axis strike at point

.
For Applying rules of reflection we have to draw a normal
As we all know, the line that strikes is circular. We can also state that normal at the sphere's surface will travel through the centre of curvature of mirror or spherical formations.
Now, according to the rules, Incident angle equals reflection angle

AS OA and OP are parallel to each other

(Alternate angle)
Also

(Reflection a

ngle)

By equation 1 and 2

When incident way come closer to principal axis then FA= FP
Also we know CF

(focal length)
Then

So, the radius of curvature is double the focal length.
Hence, the correct answer is option 1.

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