Question

Snell's law: We derive snell's law ,apparent depth of submerged object,lens formula etc from using the approximation x=tanx=sinx..thats fine.but why is tanx converted to sinx everywhere..isnt it better to stick to the more accurate form x=tanx only...is their a more accurate version of these formulae there..

Answer 1

Even i think this should not be done.. But then its done to make derivations and all easier..

Answer 2

yeah but when we derive snell's law ,how is it easier to replace tanx with sinx,mathematically they are similar functions...in case of osscilating pendulums etc the small angle approx was one thing. but to do it in optics seem weird.i mean the approx barely holds for even an angle of 20 degrees..

Answer 3

there is a value for critical angle beyond which if ur incident angle is present,then the reflected ray will beome totally internally reflected(this critical angle is between 0-90)
so there is only a narrow range of incident angles(minimum value) above which reflection takes place and snell's aw is not obeyed as refraction no longer takes place

1/sin (Ic)=refractive index of medium where incident angle is present

Answer 4

i can't find tan in snell's law.
http://en.wikipedia.org/wiki/Snell's_law
can you send me the link

Answer 5

But isnt what you said only hold when a light ray is travelling from a denser to rarer medium...when light is incident from rarer to denser medium say from air to water then incidence angle can take any value from 0 to pi radian..

Answer 6

exactly @experimentX ..that is the thing...why isnt tanx used instead of sinx..adterall using sinx instead of tanx doesnt make anything easier in the formula and the formula will be invalid for any large angle say more than 20 degree..

Answer 7

let's see how it is derived ... I been out of shape in physics.