Correct exposure for a photographic print is $10 \, s$ at a distance of $1 \, m$ from a point source of $20 \, cd$. For an equal fogging of the print placed at a distance of $2 \, m$ from a $16 \, cd$ source,the necessary time for exposure is.......$s$.

In a laboratory,a material is created with a negative refractive index. $A$ light ray enters from medium $1$ into this material (medium $2$). Which of the following diagrams correctly represents the path of the ray?

$A$ point object is kept at the first focus of a convex lens. If the lens starts moving towards the right with a constant velocity, the image will

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

$A$ 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 $20 \ cm$

For a concave mirror, if a virtual image is formed, the graph between $m$ and $u$ is of the form: