Mirror property in a straight line reflection & refraction

Reflection in the surface —

Angle of incidence = angle of reflection

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 –

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

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

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

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