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Complete Question
One day, after pulling down your window shade, you notice that sunlight is passing through a pinhole in the shade and making a small patch of light on the far wall. Having recently studied optics in your physics class, you're not too surprised to see that the patch of light seems to be a circular diffraction pattern. It appears that the central maximum is about 2 cm across, and you estimate that the distance from the window shade to the wall is about 5 m.
Required:
Estimate the diameter of the pinhole.
Answer:
The diameter is
Explanation:
From the question we are told that
The central maxima is
The distance from the window shade is
The average wavelength of the sun is mathematically evaluated as
Generally the visible light spectrum has a wavelength range between 400 nm to 700 nm
So the initial wavelength of the sun is
and the final wavelength is
Substituting this into the above equation
The diameter is evaluated as
substituting values
Answer:
a-1 Graph is attached. The relation is linear.
a-2 The corresponding height for 68 kPa Pressure is 7.54 m
a-3 The corresponding weight for 68 kPa Pressure is 1394726kg
b The original height of the column is 5.98 m
Explanation:
Part a
a-1
The graph is attached with the solution. The relation is linear as indicated by the line.
a-2
By the equation
Here
- P is the pressure which is given as 68 kPa.
- ρ is the density of the oil whose SG is 0.92. It is calculated as
- g is the gravitational constant whose value is 9.8 m/s^2
- h is the height which is to be calculated
So the height of column is 7.54m
a-3
By the relation of volume and density
Here
- ρ is the density of the oil which is 920 kg/m^3
- V is the volume of cylinder with diameter 16m calculated as follows
Mass is given as
So the mass of oil leading to 68kPa is 1394726kg
Part b
Pressure variation is given as
Now corrected pressure is as
Finding the value of height for this corrected pressure as
The original height of column is 5.98m
