In normal adujstment, for a refracting telescope, the distance between objective and eye piece is $$30 \mathrm{~cm}$$. The focal length of the objective, when the angular magnification of the telescope is 2 , will be :

A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For a light whose wavelength in air is $$\lambda$$, calculate the change of microscope's resolving power due to oil and choose the correct option.

Light travels in two media $$M_{1}$$ and $$M_{2}$$ with speeds $$1.5 \times 10^{8} \mathrm{~ms}^{-1}$$ and $$2.0 \times 10^{8} \mathrm{~ms}^{-1}$$ respectively. The critical angle between them is :

For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm from the lens. A glass plate of refractive index 1.5 and thickness 1 cm is introduced between lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen?