A simple microscope is a combination of two lenses in contact. Their powers are $+20\text{D}$ and $-4\text{D}$. The distance of distinct vision is $25\ \text{cm}$. When seen through the microscope, the size of the image of an object $3\ \text{mm}$ high is

A ray of light incident on one face of an equilateral glass prism having refractive index $\sqrt{2}$, produces the emergent ray which just grazes along the adjacent face. The value of angle of incidence is $(\sin 90^\circ = 1)$
$\left(\sin 30^\circ = \dfrac{1}{2}\right)\left(\sin 45^\circ = \dfrac{1}{\sqrt{2}}\right)$

A lens of refractive index '$\mu$' has focal length '$f$'. When the lens is immersed in a liquid of refractive index '$\mu_0$', its focal length becomes '$f_0$'. Then '$f_0$' is given by

A ray of light passes from the vacuum into a medium of refractive index 'n'. If the angle of incidence is twice the angle of refraction, then the angle of incidence in terms of refractive index is