Question
A point source has been placed as shown in the figure. What is the length on the screen that will receive reflected light from the mirror?
A point source has been placed as shown in the figure. What is the length on the screen that will receive reflected light from the mirror?
A.
$$2\,H$$
B.
$$3\,H$$
C.
$$H$$
D.
None of these
Answer :
$$2\,H$$
Solution :
$$\eqalign{ & {\text{In}}\,\Delta ABD,\frac{{BD}}{{3H}} = \tan {45^ \circ } \cr & {\text{or}}\,BD = 3H \cr} $$
And in $$\Delta A'BC,\frac{{BC}}{{2H}} = \tan \theta = \frac{1}{2}$$
$${\text{or}}\,\,BC = H$$
Now, $$y = BD - BC = 2H - H = 2H.$$
$$\eqalign{ & {\text{In}}\,\Delta ABD,\frac{{BD}}{{3H}} = \tan {45^ \circ } \cr & {\text{or}}\,BD = 3H \cr} $$
And in $$\Delta A'BC,\frac{{BC}}{{2H}} = \tan \theta = \frac{1}{2}$$
$${\text{or}}\,\,BC = H$$
Now, $$y = BD - BC = 2H - H = 2H.$$
