Question

suppose you have four transparent slabs forming a perfect pile. the thickness of the slab on top is 0.2555m, the one after is 0.5555m thick, the one after is 0.7555m thick and the one at the bottom is 1.055m thick. the indexes of refraction from top to bottom are: 1.510, 1.410, 1.310. and 1.210. a laser beam is perfectly perpendicular to the top slab and you want to know what is the OPL for the laser beam traveling exactly the four slabs vertically down. (four significant figures please.)

Answer 1

The optical path length (OPL) for the laser beam traveling through four slabs with different thicknesses and indices of refraction is calculated to be 3.435 m, rounded to four significant figures.

Step-by-step explanation:

To find the optical path length (OPL) for a laser beam traveling through the four transparent slabs, you would multiply the thickness of each slab by its index of refraction. The optical path length is given by:

OPL = (θ1 × d1) + (θ2 × d2) + (θ3 × d3) + (θ4 × d4)

Where:

• θ1 = 1.510
• θ2 = 1.410
• θ3 = 1.310
• θ4 = 1.210
• d1 = 0.2555 m (thickness of the top slab)
• d2 = 0.5555 m
• d3 = 0.7555 m
• d4 = 1.055 m (thickness of the bottom slab)

Performing the calculations:

OPL = (1.510 × 0.2555) + (1.410 × 0.5555) + (1.310 × 0.7555) + (1.210 × 1.055)

OPL = 0.3855305 + 0.7830955 + 0.9897055 + 1.27655

OPL = 3.4348815 m

Rounded to four significant figures, the OPL is 3.435 m.

It's important to note that because the laser beam is perpendicular to the slabs, no refraction occurs at the interfaces, and the original path of the light is not altered.