Fresnel S Bi-Prism

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EXPERIMENT NO. -2

Fresnel’s Bi-prism

OBJECT: To determine the wavelength of sodium light with the help of Fresnel’s Bi-prism.

APPARATUS USED: Optical bench with four uprights, a sodium lamp, a Bi-prism, a convex lens, a slit, a micrometer eye piece, and a table lamp.

FORMULA USED: Wavelength λ can be found by using formula (see figure 1.)

λ = β 2d / D

Where β = fringe width,

D = distance between the slit and micrometer eye,

2d = distance between the two virtual sources.

2d can be found by using formula (see figure 2.)

2d =

Where d1 = distance between the two images formed by the convex lens at first position (L1).

d2 = distance between the two images formed by the convex lens at second position (L2).

OBSERVATIONS:

Pitch of the screw (X) =……………..mm

Total No. of division on the micrometer screw (VS=Y) =………mm

Least count of micrometer screw (LC) = [X/Y] =

1.  DETERMINATION OF FRINGE WIDTH ‘Β’

(Note: MS = Main Scale reading, VS = Vernier Scale division.)

2. DETERMINATION OF D

Position of upright carrying slit (x1) =

Position of upright carrying eyepiece (x2) =

Therefore observed value of D ( x2 - x 1) =

3. DETERMINATION OF 2D

Ray diagram: (Should be on left page by pencil)

Calculations: (Should be on left page by pen)

From above tables we found that β = ; 2d = ; D =

Therefore, λ = β 2d / D

Results: From above measurements wavelength of sodium light found to be = ………………… (Ǻ).

Calculation for maximum probable error: (Should be on left page by pen)

λ = β 2d / D = β √ d1d2 / D

Taking log both side and differentiate

Δλ/λ = Δ β / β + ΔD / D +1/2(Δ d1 / d1) + 1/2(Δ d2 / d2)

= …………. %

[Note: Δ β = Δ d1 = Δ d1]

Sources of error and precautions:

(i) The slit should be vertical and narrow.

(ii) The setting of the uprights at the same level is essential.

(iii) Fringe shift should be removed.

(iv) The micrometer screw should be rotated only in one direction to avoid backlash error.

(v) The fringe width should be measured at a fairly large distance.

(vi) Convex lens of shorter focal length should be used (f= 25 cms. Approx.)

(vii) Motion of eyepiece should be perpendicular to the lengths of the bench.

(viii) Bench error should be taken into account.

Procedure:

Adjustments:

1. Level the bed of optical bench with the help of spirit level.

2. The slit, Bi-prism and micrometer eye piece are adjusted at the same height. The slit, edge of Bi-prism and the crosswire of micrometer eye piece are made vertical.

3. The micrometer eye piece is focused on crosswire.

4. With an opening provided to the cover of the monochromatic source, the light is allowed to incident on the slit and the bench is so adjusted that light comes straight along its length. This adjustment is made to avoid the loss of light intensity for the interference pattern.

5. Place the Bi-prism upright near the slit and move the eye piece sideway. See the two images of the slit through Bi-prism; if they are not seen, move the upright of bi-prism right angle to the bench till they are obtained. Make the two images parallel by rotating Bi-prism in its own plane.

6. Bring the eyepiece near to the Bi-prism and give it a rotation at right angle of the bench to obtain a patch of light. As a matter of fact, the interference fringes are obtained in this patch provided that the edge of the prism is parallel to the slit.

7. To make the edge of the Bi-prism parallel to the slit, the Bi-prism is rotated with the help of tangent screw till a clear interference pattern is obtained.

8. The line joining the centre of the slit and the edge of the Bi-prism should be parallel to the bed of the bench. If this is not so, there will be a lateral shift and the removal is most important. Following points keep in mind to remove lateral shift.

(a) The eyepiece is moved away from Bi-prism, and if the fringes will move to the right or left then adjusts the Bi-prism, in a direction to bring the fringes back to their original position.

(b) Now move the eyepiece towards the Bi-prism and the same adjustment is made with the help of eyepiece. By repeating the process the lateral shift is removed.

Measurements:

(A) Measurement of fringe width:

1. Find out the least count of the micrometer screw.

2. Place the micrometer screw at such a distance where fringes are distinct, bright and widely spaced, (say 100 cms.)

3. The crosswire 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 and its reading is noted on the main scale as well as on micrometer screw.

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

(B) Measurement of D:

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

(C) Measurement of 2d:

The distance 2d between the two virtual sources can be measured with the help of fig 2.

1. To obtain the value of 2d, the positions of slit and Bi-prism uprights are not disturbed.

2. A convex lens is introduced between Bi-prism and eye-piece and moved in between to obtain two sharp and focused images of the sources. The distance between two images is noted. In the first position, L1, the distance is denoted by d1.

3. The lens is again moved towards eyepiece to obtain the second position L2 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 2d = √ d1d2.