Fresnel Biprism Experiment: Measuring Light Wavelength

The Fresnel biprism is a clever device to produce two coherent sources from a single slit and observe interference fringes. It is basically two thin prisms joined base to base with a very small refracting angle. Light from a single slit is refracted by the two halves so that it appears to come from two virtual slits.

This experiment matters because it provides a school and university method to measure the wavelength of light accurately. Unlike Youngs double slit, the separation of coherent sources can be measured by imaging. The principle of division of wavefront used here is fundamental to interference optics.

Key Concepts

A biprism has an obtuse apex angle near 179 degrees and two acute angles near 0.5 degree. The virtual sources S1 and S2 are images of the single slit formed by refraction through each half. Their separation d is small, often a millimetre. Fringe width beta equals lambda D divided by d, where D is distance between virtual sources and screen or eyepiece focal plane.

• Division of wavefront creates coherence.
• Fringes are observed with a micrometer eyepiece.
• d is measured by displacement method using a convex lens.

Formulas

Fringe width beta equals lambda D divided by d. So lambda equals beta d divided by D. Separation d equals square root of d1 multiplied by d2, where d1 and d2 are separations of images of S1 and S2 in two conjugate positions of a convex lens between biprism and eyepiece. Units: lambda, beta, d, D in same length units, commonly mm converted to metres. Assumptions: slit narrow, monochromatic light, biprism edges sharp.

Worked Example

In a biprism experiment D equals 100 cm, d equals 0.20 cm and 20 fringes occupy 0.50 cm in the eyepiece. Find wavelength.

Beta equals fringe width equals 0.50 cm divided by 20 equals 0.025 cm.

lambda equals beta d divided by D equals 0.025 multiplied by 0.20 divided by 100 cm.

That equals 0.005 divided by 100 equals 5.0 times 10 to power minus 5 cm equals 5.0 times 10 to power minus 7 m equals 500 nm. This is green light, a reasonable result.

Common Misconceptions

• Biprism produces real slits: Wrong. S1 and S2 are virtual sources formed by refracted overlapping beams; there are no physical two slits.
• Any white light gives sharp fringes over large region: Wrong. White light gives only a few coloured fringes near centre due to short coherence length; monochromatic light is needed for measurement.
• d can be measured directly with scale: Wrong. Virtual sources cannot be touched; lens displacement method is used to image them.

Real-World Applications

Biprism method is a standard undergraduate method for wavelength determination and refractive index of thin sheets inserted in one beam. Modern variants use similar wavefront splitting for electron interference experiments proving wave nature of particles. Optical shops test prism angles by fringe patterns. The concept underlies Fresnel mirrors and Lloyds mirror arrangements as well.

Fresnel biprism creates two virtual coherent sources by refraction and gives lambda equals beta d divided by D. Measure beta with eyepiece, d by lens displacement and D by bench scale to get wavelength.