In the displacement method,a convex lens forms a real image of an object for its two different positions. If the heights of the images in the two cases are $24 \,cm$ and $6 \,cm$,then the height of the object is ........ $cm$.

$A$ student measures the focal length of a convex lens by placing an object pin at a distance '$u$' from the lens and measuring the distance '$v$' of the image pin. The graph between '$u$' and '$v$' plotted by the student should look like:

The power of an equi-concave lens is $-4.5 \ D$ and it is made of a material with a refractive index of $1.6$. The radius of curvature of the lens is: (in $cm$)

Monochromatic light rays parallel to $x$-axis strike a convex lens $AB$. If the lens oscillates such that $AB$ tilts up to a small angle $\theta$ (in radian) on either side of $y$-axis,then the amplitude of oscillation of the image will be ($f =$ focal length of the lens):

Write the Gaussian equation for a lens.

Assertion: $A$ double convex lens $(\mu = 1.5)$ has a focal length of $10 \, cm$. When the lens is immersed in water $(\mu = 4/3)$,its focal length becomes $40 \, cm$.
Reason: $\frac{1}{f} = \left( \frac{\mu_l - \mu_m}{\mu_m} \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$