Consider the following two cases: a) A plane mirror is kept midway between a wall and a point source. b) A point source is kept midway between a concave mirror and a wall. The radius of curvature of concave mirror, the radius of circular aperture of the two mirrors and the distance between the mirrors and wall are all equal to ‘d’. Find the ratio of radius of shadow formed on the wall in case a) and spot formed on the wall in case b)
Physics · Mixed Chapter
JEE Mains

Question

Consider the following two cases: a) A plane mirror is kept midway between a wall and a point source. b) A point source is kept midway between a concave mirror and a wall. The radius of curvature of concave mirror, the radius of circular aperture of the two mirrors and the distance between the mirrors and wall are all equal to ‘d’. Find the ratio of radius of shadow formed on the wall in case a) and spot formed on the wall in case b)

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: In case (a), the point source is d behind the plane mirror and the wall is d in front. The reflected rays diverge as if from the virtual image 2d from the wall. Step 2: The mirror aperture has radius d. By similar triangles, shadow radius on the wall = d × (2d/d) = 2d. Step 3: In case (b), the concave mirror has radius of curvature d, so f=d/2. The point source midway between the mirror and wall is at the focus. Reflected rays are parallel; the illuminated spot radius equals the apertur…