Mirror property in a straight line

Mirror property in a straight line :

Reflection in the surface —

    1. Incident ray (IP)
    2. Normal (PN)
    3. Reflected ray (PR)

Angle of incidence = angle of reflection

Reflection in the surface

Refraction in the surface —

Let assume Incident ray makes an angle θ  with tangent then refracted ray makes an angle (θ + a ) with tangent.

Where a  is an angle in opposite side after deviation.

Image of the Point in different cases -:

1.The image of the point with respect to the line mirror:

The image of the point M(x1 , y1 )  with respect to the line mirror ax + by + c = 0 be  N(x2 , y2) is given as –

The image of the point with respect to the line mirror

2.The image of the point with respect to the x-axis:

Let P ( x, y ) be any point P’( x1 , y1 ) its image after reflection on x-axis-

Then

               x1 = x

               y1  = – y

The image of the point with respect to the x-axis

3.The image of the point with respect to the y-axis:

Let P ( x, y ) be any point P’( x1 , y1 ) its image after reflection on x-axis-

Then

               x1 = -x

               y1  = y

image of a point with respect to y-axis

4.The image of the point with respect to the origin:

Let P ( x, y ) be any point P’( x1 , y1 ) its image after reflection through the origin –

Then

               x1 = – x

               y1  = – y

5.The image of the point with respect to the line y = x :

Let P ( x, y ) be any point P’( x1 , y1 ) its image after reflection on y = x –

Then

               x1 = y

               y1  = x

image of a point with respect to the line y=x

6.The image of the point with respect to the line

y = x tanθ  :

Let P ( x, y ) be any point P’( x1 , y1 ) its image after reflection on  y = x tanθ  :

Then

               x1 = x cos2θ  + y sin2θ

               y1  =  x sin2θ  – y cos2θ

6.The image of the point with respect to the line y = x tanθ - Let P ( x, y ) be any point P’( x1 , y1 ) its image after reflection on y = x tanθ