###### Advertisements

###### Advertisements

Two monochromatic rays of light are incident normally on the face AB of an isosceles right-angled prism ABC. The refractive indices of the glass prism for the two rays '1' and '2' are respectively 1.3 and 1.5. Trace the path of these rays after entering the prism.

###### Advertisements

#### Solution

Critical angle of ray 1:

`sin(c_1)=1/mu_1=1/1.3`

`=>c_1=sin^(-1)(1/1.3)=50.35^@`

Similarly, critical angle of ray 2:

`sin(c_2)=1/mu_0=1/1.52`

`=>c_2=sin^(-1)(1/1.52)=41.14^@`

Both the rays will fall on the side AC with angle of incidence *(i) *equal to 45°. Critical angle of ray 1 is greater than that of *i*. Hence, it will emerge from the prism as shown in the figure. Critical angle of ray 2 is less than that of *i. *Hence, it will be internally reflected as shown in the figure

#### APPEARS IN

#### RELATED QUESTIONS

In the wave picture of light, the intensity of light is determined by the square of the amplitude of the wave. What determines the intensity in the photon picture of light?

What kind of fringes do you expect to observe if white light is used instead of monochromatic light?

A monochromatic ray of light falls on a regular prism. What is the relation between the angle of incidence and angle of emergence in the case of minimum deviation?

Monochromatic light of frequency 5.0 × 10^{14} Hz is produced by a laser. The power emitted is 3.0 × 10^{–3 }W. Estimate the number of photons emitted per second on an average by the source ?

When monochromatic light travels from a rarer to a denser medium, explain the following, giving reasons:

(i) Is the frequency of reflected and refracted light same as the frequency of incident light?

(ii) Does the decrease in speed imply a reduction in the energy carried by light wave?

Which of the following sources provides the best monochromatic light?

The following figure shows three equidistant slits being illuminated by a monochromatic parallel beam of light. Let \[B P_0 - A P_0 = \lambda/3\text{ and }D > > \lambda.\] (a) Show that in this case \[d = \sqrt{2\lambda D/3}.\] (b) Show that the intensity at P_{0} is three times the intensity due to any of the three slits individually.

Consider the situation shown in the figure. The two slits S_{1} and S_{2} placed symmetrically around the central line are illuminated by a monochromatic light of wavelength λ. The separation between the slits is d. The light transmitted by the slits falls on a screen ∑_{1}placed at a distance D from the slits. The slit S_{3} is at the central line and the slit S_{4} is at a distance z from S_{3}. Another screen ∑_{2} is placed a further distance D away from ∑_{1}_{.}Find the ratio of the maximum to minimum intensity observed on ∑_{2} if z is equal to

(a) \[z = \frac{\lambda D}{2d}\]

(b) \[\frac{\lambda D}{d}\]

(c) \[\frac{\lambda D}{4d}\]

"Monochromatic light should be used to produce pure spectrum". Comment on this statement.

Can the interference pattern be produced by two independent monochromatic sources of light? Explain.

Monochromatic light of wavelength 650 nm falls normally on a slit of width 1.3 x 10^{-4} cm and the resulting Fraunhofer diffraction is obtained on a screen. Find the angular width of the . central maxima.

Find the angle of incidence at which a ray of monochromatic light should be incident on the first surface AB of a regular glass prism ABC so that the emergent ray grazes the adjacent surface AC. (Refractive Index of glass = 1 .56)

Monochromatic fight of wavelength 198 nm is incident on the surface of a metallic cathode whose work function is 2.5 eV How much potential difference must be applied between the cathode and the anode of a photocell to just stop the photocurrent from flowing?

**Answer the following question.**

In the diffraction due to a single slit experiment, the aperture of the slit is 3 mm. If monochromatic light of wavelength 620 nm is incident normally on the slit, calculate the separation between the first order minima and the 3rd order maxima on one side of the screen. The distance between the slit and the screen is 1.5 m.

Using the monochromatic light of the wavelength in the experimental set-up of the diffraction pattern as well as in the interference pattern where the slit separation is 1 mm, 10 interference fringes are found to be within the central maximum of the diffraction pattern. Determine the width of the single slit, if the screen is kept at the same distance from the slit in the two cases.

A monochromatic ray of light falls on a regular prism under minimum deviation condition. What is the relation between angle of incidence and angle of emergence?

For constructive interference to take place between two monochromatic light waves of wavelength λ, the path difference should be ______.

A narrow slit is illuminated by a parallel beam of monochromatic light of wavelength λ equal to 6000 Å and the angular width of the central maximum in the resulting diffraction pattern is measured. When the slit is next illuminated by light of wavelength λ’, the angular width decreases by 30%. Calculate the value of the wavelength λ’.

Monochromatic light of wavelength 396 nm is incident on the surface of a metal whose work function is 1.125 eV. Calculate:

- the energy of an incident photon in eV.
- the maximum kinetic energy of photoelectrons in eV.