Reflection from a Plane-surface

Optics of Class 12

Cartesian Sign Convention 

  1. All distances are measured from the pole.

  2. Distances measured in the direction of incident rays are taken as positive.

  3. Distances measured in a direction opposite to that of the incident rays are taken as negative.

  4. Distances above the principal axis are taken as positive.

  5. Distances below the principal axis are taken as negative.

  6. Angles measured from the normal, in anti-clockwise direction are positive, while in clockwise directions are negative.

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15.2Reflection from a Plane-surface

1.When a real object is placed in front of a plane mirror (as shown in the figure), the image is always erect, virtual and of same size as the object. It is at same distance behind the mirror as the object is infront of it. 

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An optical image is a point where reflected or refracted rays of light either intersect or appear to intersect. Thus, the image of a infinite object is an assembly of image points corresponding to various points of the object. If the rays after refraction or reflection actually converge at a point, the image is said to be real and it can be obtained on a screen. However, if the rays do not actually converge but appear to do so the image is said to be virtual. A virtual image cannot be obtained on a screen.

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2.If an object moves towards (or away from) a plane mirror at speed v, the image will also approach (or recede) at same speed v i.e., the speed of image relative to object will be v - (-v) = 2v. Similarly if the mirror is moved towards or (away from) the object with speed v the image will move towards (or away from) the object with a speed 2v.

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3.The image formed by a plane mirror suffers lateral-inversion i.e., in the image formed by a plane mirror, left is turned into right and vice-versa with respect to object as shown in figure. However, mirror does not turn upside and down and vice-versa. The reason for this is that mirror actually reverses forward and back in three-dimensions (and not left into right) − i.e., only z - direction is reversed resulting in the change of left into right or vice-versa. Actually a plane mirror changes right-handed co-ordinate system (or screw) to left handed.

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4.Deviation (δ) is defined as the angle between directions of incident ray and emergent ray. So if a ray is incident at an angle of incidence i, then the deviation is given by 

δ = 180 − (i + r) = (180 − 2i)

The deviation is maximum for normal incidence. 

δmax = 180owhen i = 0 

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5.Keeping the incident ray fixed, if the mirror is rotated through an angle θ, about an axis in the plane of mirror then the reflected ray rotates through an angle 2θ, as shown in the fig.(15.14).

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Example 15.3

A ray of light is incident at an angle of 30o with the horizontal. At what angle with horizontal must a plane mirror be placed in its path so that it becomes vertically upwards after reflection?

Solution

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