If the wavelength of light used is halved and the numerical aperture of the compound microscope is doubled, then its resolving power will

1. Remain unchanged

2. Doubled

3. Halved

4. Quadrupled

An astronaut is looking down on earth's surface from a space shuttle at an altitude of $400 km$. Assuming that the astronaut's pupil diameter is 5 mm and the wavelength of visible light is 500 nm. The astronaut will be able to resolve linear object of the size of about 

(1) 0.5 m                   

(2) 5 m

(3) 50 m                     

(4) 500 m

The average distance between the earth and moon is $38.6\times {10}^4$ km. The minimum separation between the two points on the surface of the moon that can be resolved by a telescope whose objective lens has a diameter of 5 m with $\lambda =6000\stackrel{\circ }{{\rm A}}$ is 

(1) 5.65 m                    

(2) 28.25 m

(3) 11.30 m                   

(4) 56.51 m

We wish to see inside an atom. Assuming the atom to have a diameter of 100 pm, this means that one must be able to resolved a width of say 10 p.m. If an electron microscope is used, the minimum electron energy required is about

(1) 1.5 KeV                         

(2) 15 KeV

(3) 150 KeV                       

(4) 1.5 KeV

A telescope has an objective lens of 10 cm diameter and is situated at a distance of one kilometre from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is 5000 Å, is of the order of 

(1) 0.5 m                        

(2) 5 m

(3) 5 mm                       

(4) 5 cm

The ratio of resolving powers of an optical microscope for two wavelengths ${\lambda }_1=4000 \stackrel{o}{A } and {\lambda }_2=6000 \stackrel{o}{A}$ is:

1. 8:27

2. 9:4

3. 3:2

4. 16:81

In a diffraction pattern due to a single slit of width a,the first minimum is observed at an angle ${30}^{\circ }$ when light of wavelength 5000 $\dot{A}$ is incident on the slit. The first secondary maximum is observed is an angle of 

(1) ${\sin }^{-1}\left(\frac{2}{3}\right)$

(2) ${\sin }^{-1}\left(\frac{1}{2}\right)$

(3) ${\sin }^{-1}\left(\frac{3}{4}\right)$

(4) ${\sin }^{-1}\left(\frac{1}{4}\right)$

At the first minimum adjacent to the central maximum of a single slit diffraction pattern, the phase difference between the Huygen's wavelet from the edge of the slit and the wavelet from the midpoint of the slit is

(1) π/4 radian

(2) π/2 radian

(3) π radian

(4) π/8 radian

A thin mica sheet of thickness 2×10^–6 m and refractive index (μ = 1.5) is introduced in the path of the first wave. The wavelength of the wave used is 5000 Å. The central bright maximum will shift 

(1) 2 fringes upward

(2) 2 fringes downward

(3) 10 fringes upward

(4) None of these

In Young's double slit experiment, the distance between the two slits is 0.1 mm and the wavelength of light used is 4×10^–7 m. If the width of the fringe on the screen is 4 mm, the distance between screen and slit is 

(1) 0.1 mm

(2) 1 cm

(3) 0.1 cm

(4) 1 m