Calculation of Time Taken by Sunlight to Pass Through a Window

To calculate the time taken by sunlight to pass through a window of thickness 4mm, we need to consider the principles of refraction and the refractive index of the window material.

Key Points:
- Thickness of the window: 4mm
- Refractive index of the window material: 1.5

Step 1: Determining the Speed of Light in the Window Material
The speed of light in a medium is given by the equation v = c/n, where v is the speed of light in the medium, c is the speed of light in a vacuum, and n is the refractive index of the medium.

For the given window material with a refractive index of 1.5, the speed of light in the material can be calculated as follows:

v = c/n = c/1.5

Step 2: Calculating the Time Taken
To calculate the time taken by light to pass through the window, we need to divide the thickness of the window by the speed of light in the material.

Time taken = Thickness / Speed of light in the material

Substituting the values:

Time taken = 4mm / (c/1.5)

Step 3: Converting Units and Simplifying
The thickness of the window is given in millimeters (mm), but it is preferable to use meters (m) for the calculation. Therefore, we need to convert the thickness to meters by dividing by 1000.

Time taken = (4/1000)m / (c/1.5)

Now, we can simplify the expression further by multiplying both the numerator and denominator by 1.5:

Time taken = (4/1000)m * (1.5/1.5) / (c/1.5)

Time taken = (6/1000)m / (c/1.5)

Step 4: Final Calculation
The speed of light in a vacuum is approximately 3 x 10^8 meters per second (m/s), which we can substitute as c.

Time taken = (6/1000)m / ((3 x 10^8 m/s)/1.5)

Simplifying the expression further:

Time taken = (6/1000) / ((3 x 10^8)/1.5)

Time taken = (6/1000) * (1.5/(3 x 10^8))

Time taken = 0.009 seconds

Therefore, the time taken by sunlight to pass through a window of thickness 4mm with a refractive index of 1.5 is approximately 0.009 seconds.

20 pico seconds?