A spherical generator is used to produce a -15.00D surface on glass of refractive index 1.80. The diameter of the cutting tool is 80mm and the radius of the cutting surface is 4mm. What is the angle between the axis of the tool and the axis of the lens?
Do I calculate the radius of curvature of the tool 1st?
r= n'1-n1/F
r= 1.80-1/15
r= 0.053m
r=53m ?
Can you help please?
To answer the question, you need to calculate the radius of curvature of the cutting tool first. The formula you mentioned is correct:
r = (n’ - n) / F
where:
r = radius of curvature of the tool
n’ = refractive index of the glass (1.80)
n = refractive index of the surrounding medium (assumed to be air, so n = 1)
F = power of the surface (-15.00D)
Plugging in the values:
r = (1.80 - 1) / -15.00
r ≈ -0.053 m
It seems you made a calculation error when subtracting 1.80 and 1. Keep in mind that the difference is negative because the power is negative (concave surface). The correct radius of curvature of the tool is approximately -0.053 m.
Now, to find the angle between the axis of the tool and the axis of the lens, you can use basic trigonometry. You have the radius (4 mm = 0.004 m) and diameter (80 mm = 0.08 m) of the cutting tool.
The angle between the axis of the tool and the axis of the lens can be calculated as:
θ = arctan(0.004 / (0.08/2))
First, divide the diameter by 2 to get the radius of the tool. Then, divide the radius of the cutting surface (0.004 m) by the radius of the tool (0.08/2 m). Take the arctan of this value to get the angle.
θ ≈ arctan(0.004 / 0.04) ≈ arctan(0.10) ≈ 5.71 degrees (rounded to two decimal places)
Therefore, the angle between the axis of the tool and the axis of the lens is approximately 5.71 degrees.