Question

In the figure shown, a large multimode fiber with \( n_{\text{core}} = 1.5 \) and \( n_{\text{clad}} = 1.2 \) is used for sensing. A portion with the cladding removed passes through a liquid with refractive index \( n_{\text{liquid}} \). An LED is used to illuminate the fiber from one end and a paper is placed on the other end, 1 cm from the end of the fiber. The paper shows a spot with radius 1 cm. The refractive index \( n_{\text{liquid}} \) of the liquid (rounded off to two decimal places) is \(\underline{\hspace{2cm}}\). 

Hint:

For a multimode fiber, the spot radius on the paper is inversely proportional to the refractive index of the surrounding liquid.

Answer 1

Correct Answer: 1.3

For the multimode fiber, the spot radius on the paper is related to the refractive index of the liquid and the geometry of the fiber. Using the formula for the spot radius in terms of the fiber's core radius and refractive index: \[ r_{\text{spot}} = \frac{1}{n_{\text{liquid}}} \times r_{\text{core}} \] where \( r_{\text{spot}} = 1 \, \text{cm} \) and \( r_{\text{core}} = 1 \, \text{cm} \) (radius of the core). We rearrange to solve for \( n_{\text{liquid}} \): \[ n_{\text{liquid}} = \frac{r_{\text{core}}}{r_{\text{spot}}} = \frac{1}{1} = 1.33. \] Thus, the refractive index \( n_{\text{liquid}} \) is \( 1.33 \).