Question

A microscope focused on a pin lying at the bottom of a beaker reads 3.965 cm. When a liquid is poured up to a height of 2.537 cm into the beaker, the microscope focused again on the pin reads 3.348 cm. Find the refractive index of the liquid.

Answer 1

Initial microscope reading (pin at the bottom) = 3.965 cm

Height of the liquid poured = 2.537 cm

Final microscope reading (pin’s image) = 3.348 cm

The refractive index (n) of a liquid is given by the formula:

n = `"Real depth"/"Apparent depth"`

Step 1: Calculate the real depth of the liquid.

The real depth is the actual thickness of the liquid column. This is directly given as the height of the liquid poured.

Real depth = 2.537 cm

Step 2: Calculate the apparent depth of the liquid.

The apparent depth is the perceived thickness of the liquid column from the surface. It is the difference between the real depth and the upward shift of the pin's image. The upward shift is the difference between the initial and final microscope readings.

Upward shift = Initial reading − Final reading

= 3.965 − 3.348

= 0.617 cm

Now, subtract the upward shift from the real depth to find the apparent depth.

Apparent depth = Real depth − Upward shift

= 2.537 cm − 0.617 cm

= 1.920 cm

Step 3: Calculate the refractive index of the liquid.

Using the formula, substitute the calculated values for real and apparent depth.

n = `2.537/1.920`

n ≈ 1.3211354

The refractive index of the liquid is approximately 1.321.