What is the angle of incidence for a light ray incident on a glass slab such that it does not undergo refraction (in $^{\circ}$)?

When a plane mirror is rotated through a certain angle,the reflected ray turns through twice as much and the size of the image

The image of a candle flame formed by a lens is obtained on a screen placed on the other side of the lens. If the image is three times the size of the flame and the distance between the lens and the image is $80 \, cm$,at what distance should the candle be placed from the lens? What is the nature of the image at a distance of $80 \, cm$ from the lens (in $, cm$)?

$A$ student focussed the image of a candle flame on a white screen using a convex lens. He noted down the position of the candle,screen,and the lens as under:
Position of candle $= 12.0\, cm$
Position of convex lens $= 50.0\, cm$
Position of the screen $= 88.0\, cm$
$(i)$ Where will the image be formed if he shifts the candle towards the lens at a position of $31.0\, cm$?
$(ii)$ What will be the nature of the image formed if he further shifts the candle towards the lens?
$(iii)$ Draw a ray diagram to show the formation of the image in case $(ii)$ as said above.

$A$ $2.0 \text{ cm}$ tall object is placed perpendicular to the principal axis of a convex lens of focal length $10 \text{ cm}$. The distance of the object from the lens is $15 \text{ cm}$. Find the position,nature,and size of the image formed.

Identify the device used as a spherical mirror or lens in the following cases,where the image formed is virtual and erect in each case.
$(a)$ Object is placed between the device and its focus,image formed is enlarged and behind it.
$(b)$ Object is placed between the focus and the device,image formed is enlarged and on the same side as that of the object.
$(c)$ Object is placed between infinity and the device,image formed is diminished and between the focus and optical centre on the same side as that of the object.
$(d)$ Object is placed between infinity and the device,image formed is diminished and between the pole and focus,behind it.