Question

To produce a minimum reflection of wavelength near the middle of visible spectrum (550 nm) how thick should a coating of MgF(μ = 1.38) be vacuum-coated on a glass surface?   

Solution

Correct option is

10–7

 

Consider light to be incident at near normal incidence. We wish to cause destructive interference between rays r1 and r2 so that maximum energy passes into the glass. A phase change of λ/2 occurs in each ray because at both the upper and lower surfaces of the MgF2 film the light is reflected by a medium of greater index of refraction. When striking a medium of lower index of refraction, the light is reflected with no phase change. Since in this problem both rays 1 and 2 experience the same phase shift, no net change of phase is introduced by these two reflections. Hence, the only way a phase change can occur is if the two rays travel through different optical path lengths. The optical path length is the product of the geometric path difference a ray travels through different media and the refractive index of the medium in which it is travelling. For destructive interference, the two rays must be out of phase by an odd number of half wavelengths. Hence, the optical path difference needed for destructive interference is

                              

Note that 2μd is the total optical path length that the rays transverse whenn = 0.  

SIMILAR QUESTIONS

Q1

In a double-slit experiment, two parallel slits are illuminated first by light of wavelength 400 nm and then by light of unknown wavelength. The fourth-order dark fringe resulting from the known wavelength of light falls in the same place on the screen as the second-order bright fringe from the unknown wavelength. The value of unknown wavelength of the light is 

Q2

Light is incident at an angle Ï• with the normal to a plane containing two slits of separation d. Select the expression that correctly describes the positions of the interference maxima in terms of the incoming angle Ï• and outgoing angle θ.

                                                                     

Q3

In Young’s double-slit experiment, the slits are illuminated by monochromatic light. The entire set-up is immersed in pure water. Which of the following act cannot restore the original fringe width?

Q4

Blue light of wavelength 480 nm is most strongly reflected off a thin film of oil on a glass slab when viewed near normal incident. Assuming that the index of refraction of the oil is 1.2 and that of the glass is 1.6, what is the minimum thickness of the oil film (other than zero)?

Q5

The slits in a double-slit interference experiment are illuminated by orange light (λ = 60 nm). A thin transparent plastic of thickness t is placed in front of one of the slits. The number of fringes shifting on screen is plotted versus the refractive index μ of the plastic in graph shown in fig. The value of t is

                                                  

Q6

In a YDSE with identical slits, the intensity of the central bright fringe is . If one of the slits is covered, the intensity at the same point is

Q7

The maximum intensity in Young’s double-slit experiment is I0. Distance between the slits is d = 5λ, where λ is the wavelength of monochromatic light used in the experiment. What will be the intensity of light in front of one of the slits on a screen at a distance D = d?       

Q8

Two identical coherent sources are placed on a diameter of a circle of radius R at separation x (<< R) symmetrical about the centre of the circle. The sources emit identical wavelength λ each. The number of points on the circle of maximum intensity is (x = 5λ).  

Q9

In Young’s double-slit experiment  (d = distance between slits, D = distance of screen from the slits). At a point P on the screen, resulting intensity is equal to the intensity due to the individual slitI0. Then, the distance of point P from the central maximum is (λ = 6000 Ã…)

Q10

A thin film of refractive index 1.5 and thickness 4 × 10–5 cm is illuminated by light normal to the surface. What wavelength within the visible spectrum will be intensified in the reflected beam?