Question

on a horizontal table a thin walled cylindrical glass half filled with milk is stnding upright/above the glass we place a converging lens the symmetry axis of the glass coincides with the main optical axis of the lens. the diameter ofimage of bottom of glass is same as actual glass and height of image is rwice the height of glass. what part(%) of volume of image does the milk occupy

Answer 1

50%

Answer 2

Let the cylindrical glass have radius $r$ and height $h$. The milk fills half the glass, so its height is $\frac{h}{2}$. The lens produces an image such that:

• Lateral magnification $m_{\text{lat}} = 1$ (since the image diameter equals the object’s diameter).
• Vertical magnification $m_{\text{vert}} = 2$ (since the image height is twice the glass height).

Thus, the image of the glass is a cylinder of height $2h$ and radius $r$. Under the transformation:

• The milk (object height $\frac{h}{2}$) has an image height $2 \times \frac{h}{2} = h$.

Volume of glass image: $\pi r^2 (2h)$

Volume of milk image: $\pi r^2 (h)$

Volume fraction occupied by milk:

$$\frac{\pi r^2 h}{\pi r^2 (2h)} = \frac{1}{2} = 50\%$$