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  4. A point source is placed at co-ordinates (0, 1) in X-Y plane. A ray of light from the source is reflected on a plane mirror placed along the X-axis and perpendicular to the X-Y plane. The reflected ray passes through the point (3, 3). What is the path length of the ray from (0,1 ) to (3, 3) ?

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Q. A point source is placed at co-ordinates $(0, 1)$ in $X-Y$ plane. A ray of light from the source is reflected on a plane mirror placed along the $X$-axis and perpendicular to the $X-Y$ plane. The reflected ray passes through the point $(3, 3)$. What is the path length of the ray from $(0,1 )$ to $(3, 3)$ ?

WBJEEWBJEE 2018Ray Optics and Optical Instruments

Solution:

Ray diagram for the question.
image
$I$ is image of source $S$ by the plane mirror placed perpendicularly along $X$-axis.
$\therefore SM=IM$
$\therefore PM + MS =PM + M I =PI$
$\therefore PI = \sqrt{(3-0)^2 + (3 + 1)^2}$
$= \sqrt{9 + 16} = \sqrt{25} = 5$