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Image Formation By Convex Mirror
The image formed in a convex mirror is always virtual and erect, whatever be the position of the object. In this section, let us look at the types of images formed by a convex mirror.
When an object is placed at infinity, a virtual image is formed at the focus. The size of the image is much smaller than compared to that of the object.
When an object is placed at a finite distance from the mirror, a virtual image is formed between the pole and the focus of the convex mirror. The size of the image is smaller than compared to that of the object.
Applications of curved mirrors.
- a) They are used in satellite dishes.
- b) They are used in making shaving mirrors.
- c) They are used in telescopes.
- d) They are used in driving mirrors.
Calculation of Angle of Incidence and Angle of Reflection
The angle of incidence and the angle of reflection are calculated by drawing a normal line that is perpendicular to the reflecting surface.
Q1: A ray of light is incident towards a plane mirror at an angle of 30° with the mirror surface. What will be the angle of reflection?
Since the angle of incidence is measured between the incident ray and the normal, so, here the angle of incidence is not 60°
According to the Law of Reflection,
Q2: A light ray strikes a reflective plane surface at an angle of 54° with the surface.
(i) Calculate the angle of incidence.
(ii) Calculate the angle of reflection.
(iii) Calculate the angle made by the reflected ray and the surface.
(iv) Calculate the angle made by the incident and reflected rays.
- (i) Angle of incidence, θi = 90° – 54°=36°
- (ii) Angle of Reflection, θr = 36° (As per Law of Reflection)
- (iii) Angle made by the reflected ray and the surface,
- q=90° – r = 90° – 36° = 54°
- (iv) Angle made by the incident and reflected rays,
- θi = θr =36° + 36° = 72°
- Q3:
Find angle α made by the system of the two mirrors shown in the figure below so that the incident ray at A and the reflected ray at B are parallel.
We first complete the given diagram with the angles of incidence and reflection as shown below and also labelling the incident and reflected rays.
For the incident ray at A and the reflected ray at B to be parallel, angles i + r and i’ + r’ have to be supplementary. (geometry: parallel lines cut by a transversal).
- Hence,
- i + r + i’+ r’ = 180 °
- by law of reflection : r = i and r’ = i’
- Substitute to obtain
- i + i + i’ + i’ = 180 °
- i + i’ = 90
- In triangle AOB, we have
- α + (90 – r) + (90 – i’) = 180 °
- α = r + i’ = i + i’ = 90 °
- If α = 90 °, the incident ray at A and the reflected ray at B are parallel.
Location of an image by the non-parallax method
Parallax is the apparent relative motion of two objects due to the movement of the observer.
It only occurs when the objects are at a distance from one another.
This can be used to find the position of images in plane mirrors.
Experiment: To find the position of an image of a pin by non-parallax method
Procedure
- Obtain a sheet of paper and draw a mirror line
- Place the mirror on the line as shown
- Place the pin at least 5 cm from the mirror and obtain another pin (search pin)
- Move the pin till you get a point where there is no parallax and place your second pin.
- 5. Measure the distances (both image and object) and confirm your results.
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Mirrors at an angle
When mirrors are placed at an angle several images are obtained depending on the angle between them.
If the angle is 600 the images formed will be five. We use the following formula to find the number of images.
n = (360o / θ) – 1
When mirrors are parallel then the images formed are infinite.
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Kaleidoscope
Kaleidoscope applies the principle of mirrors at an angle. Consists of two mirrors arranged at an angle of 600 to one another inside a tube.
The bottom has a ground-glass plate with brightly coloured glass for allowing light.
When one observes through the tube five images are seen.
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The periscope
The periscope consists of two mirrors arranged at an angle of 450 as shown. This principle is used in periscopes (prisms) and telescopes.