If the radius of curvature of a spherical mirror is $30 \ cm$,what is its focal length (in $cm$)?

For what position of the object does a concave mirror form a real and diminished image?

How is the refractive index of a medium related to the speed of light? Obtain an expression for the refractive index of a medium with respect to another in terms of the speed of light in these two media.

$A$ 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.

Which of the following statements is true?

An object of height $5 \, cm$ is placed perpendicular to the principal axis of a concave lens of focal length $10 \, cm$. If the distance of the object from the optical centre of the lens is $20 \, cm$,determine the position,nature,and size of the image formed using the lens formula.