An incident ray falls normally on a glass slab. What is the angle of refraction (in $°$)?

$A$ virtual image cannot be focused on a screen. Yet when we see a virtual image,we obviously bring it to the screen that is the retina of our eyes. Is this a contradiction?

$(a)$ Water has a refractive index of $1.33$ and alcohol has a refractive index of $1.36$. Which of the two media is optically denser? Give a reason for your answer. Draw a ray diagram to show the path of a ray of light passing obliquely from water to alcohol.
$(b)$ The absolute refractive index of diamond is $2.42$ and the absolute refractive index of glass is $1.50$. Find the refractive index of diamond with respect to glass.

$A$ $4.5 \, cm$ needle is placed $12 \, cm$ away from a convex mirror of focal length $15 \, cm$. Give the location of the image and the magnification. Describe what happens to the image as the needle is moved farther from the mirror.

$(a)$ Draw a ray diagram in each of the following cases to show the position and nature of the image formed when an object is placed:
$(i)$ Between the focus and the centre of curvature of a concave mirror.
$(ii)$ Between the focus and the pole of a concave mirror.
$(iii)$ Between the centre of curvature and infinity for a concave mirror.
$(b)$ Give mathematical formulae for determining the magnification produced by a spherical mirror. What does $m = -1$ signify? Identify the mirror that can produce it.

$A$ candle is placed at a distance of $10 \ cm$ from a plane mirror. At what distance from the mirror will the image of this candle be formed (in $cm$)?