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) ?

Question

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) ? (A) 5 (B) √13 (C)  2 √3 (D) 1 + 2 √3

Tardigrade Admin · Accepted Answer

Ray diagram for the question. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/20d4ba49da06ac63421971fed5412af7-.png" /> I is image of source S by the plane mirror placed perpendicularly along X-axis. ∴ SM=IM ∴ PM + MS =PM + M I =PI ∴ PI = √(3-0)2 + (3 + 1)2 = √9 + 16 = √25 = 5

$5$

$13$

$23$

$1 + 23$

Ray diagram for the question.

$I$ is image of source $S$ by the plane mirror placed perpendicularly along $X$ -axis.
$∴ SM = I M$
$∴ PM + MS = PM + M I = P I$
$∴ P I = (3 - 0)^{2} + (3 + 1)^{2}$
$= 9 + 16 = 25 = 5$

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) ?

5

13​

23​

1+23​

Ray diagram for the question. I is image of source S by the plane mirror placed perpendicularly along X-axis. ∴SM=IM ∴PM+MS=PM+MI=PI ∴PI=(3−0)2+(3+1)2​ =9+16​=25​=5

$5$

$13$

$23$

$1 + 23$

Ray diagram for the question.

$I$ is image of source $S$ by the plane mirror placed perpendicularly along $X$ -axis.
$∴ SM = I M$
$∴ PM + MS = PM + M I = P I$
$∴ P I = (3 - 0)^{2} + (3 + 1)^{2}$
$= 9 + 16 = 25 = 5$