$A$ luminous object is placed $20 \, cm$ from the surface of a convex mirror and a plane mirror is adjusted in such a way that the virtual images formed by the two mirrors coincide. If the focal length of the convex mirror is $5 \, cm$,then the distance between the plane mirror and the object will be......$cm$.

For the refraction of light through a prism,which of the following statements is correct?

When a pin is moved along the principal axis of a small concave mirror,the image position coincides with the object at a point $0.5\, m$ from the mirror. If the mirror is placed at a depth of $0.2\, m$ in a transparent liquid,the same phenomenon occurs when the pin is placed $0.4\, m$ from the mirror. The refractive index of the liquid is

$A$ ray of light strikes a plane mirror $M$ at an angle of $45^{\circ}$ as shown in the figure. After reflection,the ray passes through a prism of refractive index $1.5$ whose apex angle is $4^{\circ}$. The total angle through which the ray is deviated is......$^{\circ}$

$A$ concave mirror is placed on a horizontal table with its axis directed vertically upwards. Let $O$ be the pole of the mirror and $C$ its centre of curvature. $A$ point object is placed at $C$. It has a real image,also located at $C$. If the mirror is now filled with water,the image will be

An object is placed $60 \ cm$ in front of a convex mirror of focal length $30 \ cm$. $A$ plane mirror is now placed facing the object in between the object and the convex mirror such that it covers the lower half of the convex mirror. What should be the distance of the plane mirror from the object so that there will be no parallax between the images formed by the two mirrors (in $cm$)?