Sol. The rays reflected from the flat mirror increase the illumination at the centre of the screen. The presence of the mirror is equivalent to the appearance of a new source (with the same luminous intensity) arranged at a distance from the screen three times greater than that of the first source. For this reason the illumination should increase by one-ninth of the previous illumination, i.e.,

E a = 2.5 l x

The concave mirror is so arranged that the source is in its focus. The rays reflected from the mirror travel in a parallel beam. The illumination along the axis of the beam of parallel rays is everywhere the same and equal to the illumination created by the point source at the point of the mirror closest to it. The total illumination at the centre of the screen is equal to the sum of the illumination produced by the source at the centre of the screen and reflected by the rays:

E b = 2 × 2.25 l x = 4.5 l x

The virtual image of the point source in the convex mirror is at a distance of 2.5 r from the screen (r is the distance from the screen to the source). The luminous flux Φ emitted by the virtual source is equal to that of the real source incident on the mirror:

I 1 ω 1 = I 2 ω 2

Since the solid angle ω 1 of the flux incident on the mirror from source S (Fig.) is one-fourth of the solid angle ω 2 inside which the rays from virtual source S 1 propagate, the luminous intensity I 2 of the virtual source is one-fourth of the intensity of source S. Fro this reason the virtual source creates at the centre of the screen an illumination of 4 × (2.5) 2 = 25 times smaller that the real source. Hence, E c = 2.34 l x.