Define a ray and a beam of light.

In an experiment for the determination of focal length of a convex mirror,a convex lens of focal length $20 \ cm$ is placed on an optical bench and an object pin is placed at a distance $30 \ cm$ from the lens. When a convex mirror is introduced in between the lens and the real and inverted image of the object,the final image of the object $O$ is formed at $O$ itself. If the distance between the lens and the mirror is $10 \ cm$,then the focal length of the mirror is.......$cm$

$A$ reflecting surface is represented by the equation $y = \frac{2L}{\pi} \sin \left( \frac{\pi x}{L} \right)$,$0 \leq x \leq L$. $A$ ray travelling horizontally becomes vertical after reflection. The coordinates of the point$(s)$ where this ray is incident is?

In a movie hall,the distance between the projector and the screen is increased by $1\%$. The illumination on the screen is:

Which of the following is correct regarding microscope and telescope?

Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of the surfaces of the lenses are as given in the diagrams.