Question

A pair of crossed ideal linear polarizers allow no light to pass through. To produce some output one can insert optical elements between the crossed polarizers. For given light beam of input intensity I₀, Nirmalya inserts a quarter-wave plate between the crossed polarizers and records an output intensity αl₀. On the other hand, Ayan inserts two linear polarizer's having orientations 30° and 60° w.r.t. the first polarizers of the crossed pair, and records an output intensity of BI₀. What is the ratio α/β?

Answer 1

To produce some output with crossed ideal linear polarizers, optical elements can be inserted between them. Nirmalya uses a quarter-wave plate to change the polarization state, and Ayan uses two linear polarizers at different angles.

Step-by-step explanation:

The intensity of light passing through two crossed ideal linear polarizers will be zero because the polarizers block all light. To produce some output, we can insert optical elements between the crossed polarizers.

Nirmalya inserts a quarter-wave plate between the crossed polarizers. The quarter-wave plate changes the polarization state of the incident light, allowing some light to pass through. Nirmalya records an output intensity αI₀, where α is the transmission coefficient of the quarter-wave plate.

Ayan inserts two linear polarizers angled at 30° and 60° to the first polarizer between the crossed pair. This setup forms an 'analyzer' configuration, which allows some light to pass through. Ayan records an output intensity B*I₀, where B is the product of the transmission coefficients of the two polarizers.

To find the ratio α/β, we need to compare the two output intensities: αI₀ and BI₀. Dividing αI₀ by BI₀, we get the ratio α/β.