
Derive for a spherical mirror, where the symbols have their usual meaning.
Answer
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Hint :First law of reflection states that the incident ray, reflected ray and normal, all lie in the same plane. Second law of reflection states that the angle of reflection is always equal to the angle of incidence. The angles are measured relative to the perpendicular to the surface at the point where the ray strikes the surface.
Complete Step By Step Answer:
Let be the incident ray and be the line normal to the surface at the point where the ray strikes the surface of a spherical mirror. Let and be the focal length and radius of curvature. Also let and be the angle of incidence and the angle of reflection. Then we can draw the figure as follows
Hence and .
Also is the centre of the circle and is also the radius of the sphere.
According to second law of reflection
----(1)
Since is parallel to we get ---(2)
From the equation (1), the equation (2) becomes
Then is an isosceles triangle. Therefore ---(3)
For mirror of small aperture we get ---(4)
From the equation (3) and (4), we get
---(5)
then
.
Hence the proof.
Note :
Myopia(near-sightedness) is corrected by using a Concave Lens of suitable power. Hypermetropia(farsightedness) is corrected by using a convex lens of suitable power. A spherical mirror is a mirror which has the shape of a piece cut out of a spherical surface. There are two types of spherical mirrors: concave, and convex.
Complete Step By Step Answer:
Let

Hence
Also
According to second law of reflection
Since
From the equation (1), the equation (2) becomes
Then
For mirror of small aperture we get
From the equation (3) and (4), we get
then
Hence the proof.
Note :
Myopia(near-sightedness) is corrected by using a Concave Lens of suitable power. Hypermetropia(farsightedness) is corrected by using a convex lens of suitable power. A spherical mirror is a mirror which has the shape of a piece cut out of a spherical surface. There are two types of spherical mirrors: concave, and convex.
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