The radius of curvature of a spherical mirror is $20\, cm$. What is its focal length (in $cm$)?

$A$ convex lens forms a real and inverted image of a needle at a distance of $50\, cm$ from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also,find the power of the lens.

An object is placed at a distance of $10\, cm$ from a convex mirror of focal length $15\, cm$. Find the position and nature of the image.

The magnification produced by a plane mirror is $+1$. What does this mean?

Where should an object be placed in front of a convex lens to get a real image of the size of the object?

$A$ concave lens of focal length $15 \,cm$ forms an image $10 \,cm$ from the lens. How far is the object placed from the lens? Draw the ray diagram.