To find the wavelength of Sodium light by Fresnels biprism experiment.

AIM

Optical bench with uprights APPARATUS REQUIRED Sodium lamp

BiprismLens

The wavelength of the sodium light is given by the formula in case of biprismexperiment. = *2d DWhere, = fringe width, 2d = distance between the two virtual sources, D = distance between the slit and screen. 2d = (d1d2)Where , d1 = distance between the two images formed by the convex lens in the first position. d2 = distance between the two images formed by the convex lens in the second position.

FORMULA USED

The Fresnel biprism is a prism which has one of its angles slightly less than two right angles and two equal small base angles. It acts like two very thin prisms placed base to base. When rays from a slit , S, illuminated by a monochromatic light, such as sodium light are made to be incident on the plane face of the biprism , the emergent rays from the two halves of the biprism appear to diverge from two coherent virtual sources, S1 and S2.

THEORY

If a screen is placed with its plane perpendicular to the plane containing the slit and the common base of the biprism, the emergent beams of light overlap on the screen producing alternate dark and bright fringes.

If d is the distance between the two virtual sources S1 and S2,Dis the distance between the slit and the screen, and is the wavelength of the monochromatic radiation, then the fringe width, x i.e., the distance between two consecutive dark or bright fringes is given by

To determine d , a convex lens having such a focal length that the distance between the slot and the focal plane of the eye-piece exceeds four times the focal length is interposed between the biprism and the eye-piece. The lens is adjusted so that for two of its positions the real images of the two virtual sources S1 and S2 are focused on the focal plane of the eye-piece. If d1 and d 2 are the distances between the real images of S1 and S2 for two positions of the lens, then 2d = (d1 d2)

PROCEDUREMeasurement of fringe width ():Find out the least count of the micrometer screw.

ii) Place the micrometer screw at such a distance from bi prism where fringes are distinct , bright and widely spaced, say 120 cms .

iii) The cross wire is moved on one side of the fringes to avoid backlash error. Now the cross wire is fixed at the centre of a bright fringe.

iv) The crosswire is now moved and fixed at the centre of every second fringe. The micrometer readings are noted. From these observations can be calculated.

Measurement of 2d:The distance 2d between the two virtual sources can be measured with the help of fig.To obtain the value of 2d, the positions of slit and Bi-prism uprights are not disturbed.

ii) A convex lens is introduced between Bi-prism and eye-piece and moved in between to obtain the second position where again two sharp and focused images are obtained. The distance between two images is noted. In the first position the distance is noted by d1.

Measurement of D:The distance between the slit and eyepiece uprights is noted. This distance gives D . The value of D is corrected for the bench error.

iii) The lens is again moved towards the eye-piece to obtain the second position where again two sharp and focused images are obtained. The distance in this case is denoted by d2. Knowing d1 and d2 , 2d can be calculated by using the formula:

Therefore, value of D=50cm = 500mmMEASUREMENT OF DLeast count of vernier scale= 0.1mm= 0.01cm OBSERVATIONS

POSITION OF SLIT (cm) POSITION OF EYEPIECE (cm) OBSERVED VALUE (cm)

Main ScaleVernier ScaleTotalMain ScaleVernier ScaleTotal 170 0 170 120 0 120 50

MEASUREMENT OF 2d Pitch of screw = 0.5 mm no. of divisions = 100 least count of screw = 0.005mm

MICROMETER READING (cm)

First Image Second Image d1 & d2

MSR VSR TSR MSR VSR TSR 8.5 59 8.795 7.0 36 7.180 d1=1.614 6.0 36 6.180 5.5 50 5.750 d2=0.430

MEASUREMENT OF Mean separation for 10 fringes = 3.600mmMean separation for 1 fringe = 0.360mm

NO. OF FRINGESMICROMETER READING a (mm)NO. OF FRINGESMICROMETER READING b (mm)SEPARATION OF 10 FRINGES (b-a) 1 8.100 11 4.400 3.700 6 6.200 16 2.400 3.800 11 4.400 21 1.050 3.350

RESULT Wavelength of sodium light = 599. 7 mm

Standard value of = 589.3 mm

Percentage Error = 1.764 %

Precautions and Sources of Error:

i) The setting of uprights at the same level is essential.ii) The slit should be vertical and narrow.iii) Fringe shift should be removed.iv) Bench error should be taken into account.v) Crosswire should be fixed in the center of the fringe while taking observations for fringewidth.vi) The micrometer screw should be rotated only in one direction to avoid backlash error.

Used in stereo camera system used in single lens stereo

Applications in Real World

Bibliographyhttp://en.wikipedia.org/wiki/Common_path_interferometer#Fresnel.27s_biprism

Engineering physics by Devraj Singh

BySahil BajajSahil MungiaSaras GuptaShailendra