$A$ double convex lens has two surfaces of equal radii $15 \, cm$ and refractive index $\mu = 1.5$. Its focal length is equal to ..... $cm$.

$A$ square card of side length $1\, mm$ is being seen through a magnifying lens of focal length $10\, cm$. The card is placed at a distance of $9\, cm$ from the lens. The axis is perpendicular to the plane of the card. The apparent area of the card through the lens is......$cm^2$

Write the lens maker's equation for a thin lens.

When light rays from the sun fall on a convex lens along a direction parallel to its axis,which of the following statements is true?

An object is moving with a velocity $V_O = 4 \text{ cm/sec}$ towards a convex lens of focal length $f = 10 \text{ cm}$. The lens is also moving with a velocity $V_L = 2 \text{ cm/sec}$ in the same direction. At the instant when the object is at a distance of $30 \text{ cm}$ from the lens,find the velocity of the image.

Derive the thin lens equation.