Ray diagrams of reflection of light
1
In the figure, 1 and 2 are the incident rays while 1l and 2l are the rays emerging from the region PQRS. Complete the diagram showing the optical object inside the region PQRS, producing this effect?
Sol:
In the above figure the emergent rays are diverging on the same side, therefore there must be a convex mirror inside PQRS. The focus of the mirror will coincide with the point of intersection of the rays 1l and 2l when they are produced backwards. The complete ray diagram is shown below figure.
2
In the given figure, PQ is the object, P1Q1 is its image, and MMl is a spherical mirror. Complete the ray diagram and find the position of the centre of curvature and focus of the mirror.Measure the focal length?
Sol:
The image P1Q1 formed behind the mirror. Therefore, it is a virtual and erect image. Also, it is clear from the figure that it is a diminished image. Therefore, the mirror MMl is convex.
We can complete the ray diagram as follows.
Steps to complete the diagram.
(i) Draw one ray from P parallel to the principal axis upto the mirror. Join the point of intersection B with P1 and produce it upto the principal axis. The point where it meets the principal axis is the principal focus F.
(ii) Draw another ray joining the points P and P1.
(iii) The point where this ray meets the principal axis, is the centre of curvature C.
The distance OF is the focal length. F and C are the positions of center of curvature and principal focus respectively.
3
In the figure, XY is the object, X1Y1 is its image and MMl is the position of the mirror. Complete the ray diagram to show the formation of the image.
Sol:
Here, the image X1Y1 is virtual, erect and magnified. Therefore, the mirror MMl is concave.
We can complete the ray diagram as follows.
The ray diagram completed is shown below.
C and F are the positions of the centre of curvature and focus respectively. OF is the focal length.
4
In the below figure, PQ is the object, P1Q1 is the image and MMl is the position of the mirror. Complete the ray diagram showing the formation of the image.
Sol:
Here, the image P1Q1 is real, inverted and diminished. Therefore, the mirror MMl is concave.
The ray diagram completed is shown below.
C and F are the positions of the centre of curvature and principal focus respectively.
OF is the focal length.