Assume that light of wavelength 6000Å is coming from a star. What is the limit of resolution of a telescope whose objective has a diameter of 100 inches?

$$\begin{gathered} 1.<mspace\; width="1em"></mspace>1.2\times {10}^{-6}<mspace\; width="1em"></mspace>\mathrm{radians} \\ 2.<mspace\; width="1em"></mspace>3.3\times {10}^{-7}<mspace\; width="1em"></mspace>\mathrm{radians} \\ 3.<mspace\; width="1em"></mspace>1.7\times {10}^{-6}<mspace\; width="1em"></mspace>\mathrm{radians} \\ 4.<mspace\; width="1em"></mspace>2.9\times {10}^{-7}<mspace\; width="1em"></mspace>\mathrm{radians} \end{gathered}$$

The resolving power of a compound microscope will be maximum when:

For what distance is ray optics a good approximation when the aperture is \(3\) mm wide and the wavelength is \(500\) nm?
1. \(32\) m
2. \(42\) m
3. \(18\) m
4. \(20\) m

The ratio of resolving powers of an optical microscope for two wavelengths ${\lambda }_1$=4000 $\stackrel{0}{A}$ and ${\lambda }_2=6000$ $\stackrel{0}{A}$ is:

1. 9:4

2. 3:2

3. 16:81

4. 8:27

Assume that light of wavelength 600 nm is coming from a star. The limit of resolution of telescope whose objective has a diameter of 2 m is:

1. $1.83\times {10}^{-7}$ $rad$

2. $7.32\times {10}^{-7}$ $rad$

3. $6.00\times {10}^{-7}$ $rad$

4. $3.66\times {10}^{-7}$ $rad$

A major breakthrough in the studies of cells came with the development of an electron microscope. This is because:

The graph between resolving power and accelerating potential V for an electron microscope is (P is resolving power):

1.		2.
3.		4.

Given below are two statements: 

Resolving power of a compound microscope:

1.  Depends on the wavelength of light as \(\propto\) $\lambda$

2.  Depends on the wavelength of light as \(\propto\) $\lambda$²

3.  Depends on the wavelength of light as \(\propto\) $\frac{1}{\lambda }$

4.  Depends on the wavelength of light as \(\propto\) $\frac{1}{{\lambda }^2}$

The ratio of resolving powers of an optical microscope for two wavelengths ${\lambda }_1=4000<mspace\; width="1em"></mspace>\stackrel{o}{A<mspace\; width="1em"></mspace>}<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>{\lambda }_2=6000<mspace\; width="1em"></mspace>\stackrel{o}{A}$ is:

1. 8:27

2. 9:4

3. 3:2

4. 16:81