$A$ convex mirror and a concave mirror of radius $10\; cm$ each are placed $15\; cm$ apart facing each other. An object is placed midway between them. If the reflection first takes place in the concave mirror and then in the convex mirror,the position of the final image is:

$A$ lamp is hanging $1 \, m$ above the center of a circular table of diameter $1 \, m$. The ratio of illuminances at the center and the edge is:

$A$ biconvex lens $(R_1 = R_2 = 30 \ cm)$ has a focal length equal to the focal length of a concave mirror. What is the radius of curvature of the concave mirror (in $cm$)? (Refractive index of the material of the lens $\mu = 1.6$)

$A$ plano-convex lens is made of a material of refractive index $n$. When a small object is placed $30 \ cm$ away in front of the curved surface of the lens,an image of double the size of the object is produced. Due to reflection from the curved surface of the lens,another faint image is observed at a distance of $10 \ cm$ away from the lens. Which of the following statement$(s)$ is(are) true?
$(A)$ The refractive index of the lens is $2.5$
$(B)$ The radius of curvature of the convex surface is $45 \ cm$
$(C)$ The faint image is erect and real
$(D)$ The focal length of the lens is $20 \ cm$

$A$ ray of light falls on the surface of a spherical glass paperweight,making an angle $\alpha$ with the normal,and is refracted in the medium at an angle $\beta$. What is the angle of deviation of the emergent ray from the direction of the incident ray?

If the focal length of the objective lens is increased,then: