A microscope is focused on a mark a table, when the mark is covered by a glass 3.00cm thick. Tthe microscope has to be raised 1.1cm for the mark to be once more in focus. Calculate the refractive index of the glass.

To calculate the refractive index of the glass, we need some basic information and formulas. Here's how you can solve the problem:

1. Recall the formula for the refractive index of a medium:
Refractive index (n) = speed of light in vacuum (c) / speed of light in the medium (v)

2. Determine the speed of light in vacuum:
The speed of light in a vacuum is a constant value, approximately 3.00 x 10^8 meters per second (m/s).

3. Calculate the speed of light in the glass:
The speed of light in a medium can be calculated using the equation:
Speed of light in medium (v) = c / refractive index (n)

4. Calculate the change in distance the microscope needs to be raised:
The microscope needs to be raised by 1.1 cm to refocus the mark. Convert this value to meters by dividing by 100:
Change in distance (d) = 1.1 cm / 100 = 0.011 m

5. Calculate the total distance traversed by light in the glass:
Since the microscope needs to be raised, the light has to travel a longer path in the glass. This total distance is given by:
Total distance in glass (L) = thickness of the glass (t) + change in distance (d)

6. Use the formula for refractive index to find the value:
Refractive index (n) = c / v
Substitute v with the speed of light in glass (v = c / n)
and rearrange the formula:
n = c / (c / n)
n = (c * n) / c
n = n

7. Substitute the values into the formula:
n = c / (c / n)
n = (3.00 x 10^8 m/s) / [(3.00 x 10^8 m/s) / (L)]
n = (3.00 x 10^8 m/s) / [(3.00 x 10^8 m/s) / (0.011 m + 0.03 m)]

8. Calculate the refractive index:
Simplifying the expression, we get:
n = (3.00 x 10^8 m/s) / (3.00 x 10^8 m/s) * (1 / (0.11 m + 0.03 m))
n = (3.00 x 10^8 m/s) / (3.00 x 10^8 m/s) * (1 / 0.14 m)
n = (1 / 0.14)

9. Calculate the refractive index value:
Using a calculator, the refractive index of the glass comes out to be:
n ≈ 7.142

Therefore, the refractive index of the glass is approximately 7.142.