The circular boundary of the concave mirror s | vedclass

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(B) For a ray incident parallel to the principal axis to undergo multiple reflections,it must strike the mirror at a point such that after the first r

Vedclass · Accepted Answer

$45$

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(B) For a ray incident parallel to the principal axis to undergo multiple reflections,it must strike the mirror at a point such that after the first reflection,it is directed towards another point on the mirror.Consider a ray incident at the edge of the mirror. After reflection,the angle of incidence equals the angle of reflection. The normal at any point on the spherical mirror passes through the centre of curvature $C$.For the ray to hit the other end of the mirror after the first reflection,the reflected ray must make an angle of $90^{\circ}$ with the incident ray (which is parallel to the principal axis). From the geometry of the reflection,the angle between the normal and the reflected ray is $	heta$. The angle between the incident ray and the normal is also $	heta$. Thus,the angle between the incident ray and the reflected ray is $2	heta$. For the reflected ray to be perpendicular to the incident ray,we must have $2	heta = 90^{\circ}$.Therefore,$	heta = 45^{\circ}$.

The circular boundary of the concave mirror subtends a cone of half-angle $\theta$ at its centre of curvature. The minimum value of $\theta$ for which a ray incident on this mirror parallel to the principal axis suffers more than one reflection is......$^o$

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