To determine the wavelength of light using a plane diffraction grating by measuring the Angle of minimum deviation.

Aim

To determine the wavelength of light using a plane diffraction grating by measuring the Angle of minimum deviation.

Apparatus Required

Plane diffraction grating, spectrometer, reading lens, sodium vapor lamp.

Principle

If a parallel beam of monochromatic light is incident on a grating, such that the angle of deviation is minimum, the relation gives the wavelength of the light.

λ = 2 sin(D / 2)/Nη

Where, D is the angle of minimum deviation

η is the order of the spectrometer

N is the number of lines per cm

Procedure

1. The preliminary adjustments of the spectrometer are done. The slit is illuminated with Sodium light.
2. The grating is clamped to the prism table. The plane of the grating is adjusted to be Vertical and perpendicular to the axis of the collimator.
3. The direct image of the slit is observed through telescope and by fine adjustment of the tangent Screw of the telescope, the point of intersection of the cross wire is set on the image of the slit. The readings of the two verniers are noted.
4. The telescope is moved to the left to observe the diffracted image of the first order.
5. The prism table is released and is rotated to the left. Then the first order image moves. To the right, reaches a limiting position, and then tries to retrace its path.
6. The telescope is fixed in this limiting position such that the point of intersection of the Cross wire is on the D1 line. The readings on both the verniers are noted.
7. The respective difference on the verniers gives the minimum deviation for the D1 line. Similarly the experiment is repeated on the right hand side for the first order D1 line. The experiment is repeated for D2 line.

Observations

The observations of the experiment are as follows

Least count of spectrometer = 1 MSD / Number of diviations in vernier scale

No. of lines per cm. on the grating (N) =

Table

Calculations

λ = 2 sin(D / 2)/Nη

Where, D is the angle of minimum deviation

η is the order of the spectrometer and

N is the number of lines per cm

Precautions

1. The grating should be adjusted for each order separately.
2. Readings are noted without any parallax error.

Result

Wave length of sodium is ................ A⁰(I^st order)

Wave length of sodium is ................ A⁰(II^nd order)