For the triangle shown at below, what is the angle theta in radians and in degre

Question

For the triangle shown at below, what is the angle theta in radians and in degrees? 2. What would be your answers if you made the small angle approximation (sin theta = tan theta = theta)? What would be your % error in theta if you made the small angle approximation? Why is it OK to stare at a 100 watt light bulb, considering that a 0.001 watt laser aimed into your eye will damage it? (Try to answer beyond just "it's brighter" or "it's more damaging", we are curious how you would explain why? After all, the laser power is 100,000 times smaller, how might a physicist explain this apparently curious fact?)

Explanation / Answer

1)

tan(theta) = 0.04/1 = 0.04

theta = 2.2906 degree

2)

tan(theta) = theta = 0.04 rad = 0.04 * 180 /pi = 2.2918

error in measure = (2.2918 - 2.2906)*100 / 2.2906 = 0.052 %

3)

how is laser light different?

First, the light from a laser contains exactly one color or wavelength rather than a lot of different wavelengths. Scientists say that laser light is "monochromatic," meaning of one color.

Second, all the wavelengths are in phase. That is, they are all "waving" together, like a well-timed audience "wave" at a football game. All the wave crests (high points) and troughs (low points) are lined up. Scientists say the laser light is "coherent."

And third, while light waves from ordinary sources (such as flashlights, lightbulbs, or the Sun) spread out in all directions laser light waves all travel in the same direction, exactly parallel to one another. This means that laser light beams are very narrow and can be concentrated on one tiny spot. Scientists say the laser light is "collimated."

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