Power of a lens increases if red light is replaced by violet light because \(\\ \\ P=\cfrac { 1 }{ f } \left( _{ a }{ n }_{ g }-1 \right) \left( \cfrac { 1 }{ { R }_{ 1 } } -\cfrac { 1 }{ { R }_{ 2 } } \right) \) and refractive index is maximum for violet light in visible region of spectrum.

Yes, since magnification depends upon the focal length and focal length depends on the color and different colours have different wavelengths (i.e., different refractive indices.)
\(\cfrac { 1 }{ f } =\left( \mu -1 \right) \left( \cfrac { 1 }{ { R }_{ 1 } } -\cfrac { 1 }{ { R }_{ 2 } } \right) \) 
(By Lens Makers Formula) Also, magnification of the compound microscope
\(M=\cfrac { -L }{ { f }_{ o } } \left( 1+\cfrac { D }{ { f }_{ e } } \right) \)

Scattering of light: When light falls on fog then scattering takes place so the particles of fog becomes visible. Visible light cannot pass through fog.

For relaxed eye, L = f₀ + f_e.
for least distance of distinct vision
L' = f₀ + u_e, u_e e
Therefore, L' < L, that is, the distance will be decreased.

(i) Fringe width of interference fringes is given by \(\beta =\cfrac { D\lambda }{ d } \propto \cfrac { 1 }{ d } \) When d is infinitely small, fringe width β will be too large.
(ii) In such a case even a single fringe may occupy the whole field of view. Hence, the interference pattern cannot be detected.

(i) Fringe width of interference fringes, is given by \(\beta =\cfrac { D\lambda }{ d } \propto \cfrac { 1 }{ d } \) . If the sources are far apart, d is large; so fringe width (β) will be so small that the fringes are not resolved and they do not appear separate.
(ii) That is why the interference pattern is not detected for large separation of coherent sources.

The phenomenon of addition or superposition of two light waves which produces increase in intensity at some points and decrease in intensity at some other points is called interference of light.

(i) It produces plane polarised light and functions as a polariser.
(ii) It can also be used to analyse the plane polarised light i.e used at an analyser.

The angular resolution has a unit in radian (rad) and it is given by the equation,
\(\theta =\cfrac { 1.22\lambda }{ \alpha } \)

The combined width of a ruling and a slit is called grating element (e = a + b). Points on successive slits separated by a distance equal to the grating element are called corresponding points.

The bandwidth (β) is defined as the distance between any two consecutive bright or dark fringes.

(i)If the crest of one wave meets the trough of the other wave and vice versa, the waves are out-of-phase.
(ii) At these points, the displacement is minimum and these points appear dark. This is known as destructive interference.

(i) If the crest of one wave meets the crest of the other wave or the trough of one wave meets the trough of the other wave, the waves are in-phase.
(ii) At these point, the displacement is maximum and these points appear bright. This is known as constructive interference.

Real image :
This type of image which can be formed on a screen and can also be seen with the eyes is called real image.
Virtual image :
Image which cannot be formed on the screen but can only be seen with the eyes.

(i) If the scattering of light is by atoms and molecules which have size a very less than that of the wavelength λ of light a <.
(ii) The intensity of Rayleigh's scattering is inversely proportional to the fourth power of wavelength.
\(1\propto \cfrac { 1 }{ { \lambda }^{ 4 } } \)