 For a spherical mirror, the relationship between the radius of curvature (R) and the focal length (f) is given by the formula f= R/2. If the radius of curvature of a spherical mirror is 20 cm, its focal length can be calculated as f = 20/2 =10 cm.
Therefore, the focal length of the spherical mirror is 10 cm. This relationship holds true for both concave and convex mirrors.

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## Understanding the Radius of Curvature

Basic Concept: The radius of curvature of a spherical mirror refers to the radius of the imaginary sphere of which the mirror’s surface forms a part. It is a key parameter in defining the mirror’s curvature and optical properties.

### Relationship between Radius of Curvature and Focal Length

Fundamental Optical Principle: The focal length of a spherical mirror is directly related to its radius of curvature. This relationship is expressed by the formula f = R/2, where f is the focal length and R is the radius of curvature.

#### Calculation of Focal Length

Applying the Formula: Given a spherical mirror with a radius of curvature of 20 cm, we apply the formula to find the focal length. By substituting R=20 cm into the formula f = R/2, we get f =20/2 = 10 cm

##### Result of the Calculation

Determining Focal Length: From the calculation, the focal length of the mirror is found to be 10 cm. This means that parallel rays of light, after reflecting off the mirror, will converge or appear to diverge from a point 10 cm from the mirror’s surface.

###### Implications in Optical Design

Significance in Optics: The focal length is crucial in designing optical systems, as it determines how the mirror will focus light. A 10 cm focal length is a common specification in various optical applications, including telescopes, cameras, and other imaging devices.

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Questions of 10th Science Chapter 9 in Detail

 Define the principal focus of a concave mirror. The radius of curvature of a spherical mirror is 20 cm. What is its focal length? Name a mirror that can give an erect and enlarged image of an object. Why do we prefer a convex mirror as a rear-view mirror in vehicles? Find the focal length of a convex mirror whose radius of curvature is 32 cm. A concave mirror produces three times magnified (enlarged) real image of an object placed at 10 cm in front of it. Where is the image located? A ray of light travelling in air enters obliquely into water. Does the light ray bend towards the normal or away from the normal? Why? Light enters from air to glass having refractive index 1.50. What is the speed of light in the glass? Find out, from Table, the medium having highest optical density. Also find the medium with lowest optical density. You are given kerosene, turpentine and water. In which of these does the light travel fastest? The refractive index of diamond is 2.42. What is the meaning of this statement? Define 1 dioptre of power of a lens. A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Find the power of a concave lens of focal length 2 m. We wish to obtain an erect image of an object, using a concave mirror of focal length 15 cm. What should be the range of distance of the object from the mirror? Name the type of mirror used in the following situations. (a) Headlights of a car. (b) Side/rear-view mirror of a vehicle. (c) Solar furnace. One-half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object? An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. What is the position, size and the nature of the image formed. A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image. The magnification produced by a plane mirror is +1. What does this mean? An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size. An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained? Find the focal length of a lens of power – 2.0 D. What type of lens is this? A doctor has prescribed a corrective lens of power +1.5 D. Find the focal length of the lens. Is the prescribed lens diverging or converging?