Angle of incidence for HD-DVD




I’m looking for the angle of incidence of the HD-DVD optical system.

I know the formula to calculate the numeric aperture:

NA = n * sin(u)

n is the refractive index and u the angle of incidence. We all know, that the NA of HD-DVD is 0.65. The refractive index is 1.62. So I could change the equation to

NA/n = sin(u)
0.65/1.62 = sin(u)

But my mathematics lessons are really to long ago, so I don’t know how to depatch the equation. By using a loop to solve the problem by testing, I get different results for u, where the NA is 0.65 and the refractive index is 1.62.

Can anyone help me?




Welcome to the forum :slight_smile:

If you know the sine to an angle, but not the angle itself, all you need to do is get the inverse sine of the value to get the angle.

So, if you take 0.65/1.62 = sin(u), then get the inverse sine of both ends, the equation works out as:

è Sin<SUP>-1 </SUP>(0.65 / 1.62) = u

First perform the calculation within the brackets:

è Sin<SUP>-1 </SUP>(0.40123) = u

Before you perform the calculation, be sure to set your calculator in Degrees or Radians, depending on what you want. In this case, I assume you want your angle in degrees. To work in degrees on a calculator, set it to the ‘Deg’ mode. For Windows, tick the ‘Degrees’ button in the Windows Calculator. To perform an inverse sine, press the ‘inv’ button on your calculator before pressing ‘sin’ button. Some scientific calculators have a 'sin<SUP>-1</SUP>’ on them above the ‘sin’ key, which can be used by first pressing the ‘2nd’ button. With the Windows calculator, first set it to scientific mode (View è Scientific), tick the ‘Inv’ option to perform an inverse operation, type in the value to get the inverse sine of and finally press the ‘sin’ button.

è 23.655 = u


Godd Morning Seán!

Thank you very much for your detailed explaining. I knew, that there was something with the calculator, but as I said in the beginning: it is too long ago.