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 plane mirror?

• A. $2H$
• B. $H$
• C. $3H$
• D. $\frac{H}{2}$

Answer 1

The correct option is A $2H$

Let the given condition be geometrically represented as shown below
From the geometry we can see that $CD$ is the length on the screen that will receive reflected light from the plane mirror.
In $\Delta ABD,\tan {45}^{\circ }=\frac{BD}{AB}=\frac{BD}{3H}$
$\Rightarrow BD=3H...\left(i\right)$
Also, from $\Delta O{A}^{\text{'}}{S}^{\text{'}}$ we have
$\tan \theta =\frac{O{S}^{\text{'}}}{O{A}^{\text{'}}}=\frac{H}{2H}=\frac{1}{2}...\left(ii\right)$
And from $\Delta A^{\text{'}}BC$ we have
$\tan \theta =\frac{BC}{A^{\text{'}}B}=\frac{BC}{2H}...\left(iii\right)$
From eq $\left(ii\right)\text{and}\left(iii\right)$ we have
$\frac{BC}{2H}=\frac{1}{2}\Rightarrow BC=H...\left(iv\right)$
Thus, we get from eq $\left(i\right)\text{and}\left(iv\right)$
$y=CD=BD-BC=3H-H=2H$