What is the mirror formula for a spherical mirror?

Define lateral magnification.

$(a)$ Explain the following terms related to spherical lenses:
$(i)$ Optical centre
$(ii)$ Centres of curvature
$(iii)$ Principal axis
$(iv)$ Aperture
$(v)$ Principal focus
$(vi)$ Focal length
$(b)$ $A$ converging lens has a focal length of $12 \, cm$. Calculate at what distance should the object be placed from the lens so that it forms an image at $48 \, cm$ on the other side of the lens.

When a plane mirror is rotated by an angle $\theta$,the reflected ray turns by an angle $2\theta$. Is this statement true or false?

The figure below shows a lens treated as a combination of two prisms and a glass block. $(i)$ Name the lens formed by the combination. $(ii)$ Is the lens converging or diverging? $(iii)$ Draw the refraction of two incident rays to illustrate the property of the lens mentioned by you in part $(ii).$

If the image formed by a mirror for all positions of the object placed in front of it is always erect and diminished,what type of mirror is it? Draw a ray diagram to justify your answer. Where and why do we generally use this type of mirror?