Jyothishraj IMS12058 09th & 10th Jan, 15

EXPERIMENT NO: 1 : Velocity of Light Foucaults method

AIM To measure the velocity of light in air by Foucaults method.

APPARATUS High speed rotating mirror assembly, Fixed mirror, Micrometer setup, beam-splitter, 0.5mW He-Ne laser, biconvex lenses(252 mm, 48 mm), polarisers, alignment jigs, optical bench, laser alignment bench, bench couplers, component holders, measuring tape, power supply.

THEORY Measuring the velocity of light has been one of the most intriguing challenges scientists had faced for a long time. Here, we try to use the same technique as Foucault [in 1862], which uses 2 mirrors, one fixed & the other rotating at a constant angular velocity. The experimental setup can be schematically given as

The parallel beam of light from the laser is focused to a point image at point s by lens L1. Lens L2 is positioned so that the image point at s is reflected from the rotating mirror MR, and is focused onto the fixed, spherical mirror MF. MF reflects the light back along the same path to again focus the image at point s. A beam splitter is placed in the optical path, so a reflected image of the returning light is also formed at point s. Now MR is rotated continuously at a very high speed. In this case, the return image of the source point will no longer be formed at s and s. This is because, with MR rotating, a light pulse that travels from MR to MF and back finds MR at a different angle when it returns than when it was first reflected. By measuring the displacement of the image point caused by the rotation of MR, the velocity of light can be determined.

Where c = speed of light

w = rotational velocity of rotating mirror A = distance between L1 & L2, minus the focal length of L1 B = distance between L2 & rotating mirror D = distance between rotating & fixed mirrors s = displacement of the image point (in micrometer scale)

An alternate form that can be used is

Where the measurements are done for clockwise (cw) & counter-clockwise (ccw) rotations, and the corresponding displacements are used. Also, the w is converted to radians per second form. OBSERVATIONS The distances were set as A = 0.307 m, B = 0.457 m, D = 3.03 m and the clockwise & counterclockwise displacements were observed as follows

TRIAL NO. w (cw) [in rps] s(cw) [in mm] w (ccw) [in rps] s(ccw) [in mm] c [* 108 ms-1] % error 1 616 11.06 609 10.96 2.4886 16.98 2 615 10.95 629 10.86 2.8079 6.33 3 811 10.97 818 10.83 2.3638 21.15 4 820 11.08 828 10.98 3.3479 11.67 5 1006 10.98 1005 10.80 2.2696 24.29 6 1019 11.11 1008 11.00 3.7435 24.87

Mean velocity of light = ( 2.837 + 0.54 ) x 108 ms-1 Trial with minimum error yielded c = 2.8079 x 108 ms-1 ( 6.33 % error ) RESULTS The velocity of light is measured by Foucaults method and is found to be ( 2.837 + 0.54 ) x 108 ms-1 . THE EXTRA BIT AIM- To find out the angular velocity of the rotating mirror using a photodiode/photodetector apparatus coupled to the rotating mirror assembly. PROPSED EXPERIMENT The laser was aligned as earlier and the mirror was set a constant w. The reflected beam was made to fall on the photodetector, and the instantaneous output current was observed in the display. The output current could be then fed to a CRO to visualise & quantify the oscillatory nature, from which the time period & frequency of rotation can be calculated.

OBSERVATIONS & FOLLOW-UP- The current output was sure fluctuating, but the sensitivity of the detector was quite low to detect even low w. The reason was that the current produced was too less to be visualised in the CRO. So, it was proposed that we design & construct an amplifier for the same, which can then be coupled to the existing setup, so that the output current can be visualised in the CRO to deduce the w. The follow-up and completion of the modified experiment will be done along with the coming electronic experiments with amplifiers.