if the refractive index of air to glass is 1.52 and air to water is 1.33 than find the density of the glass if density of water is 1g/cm^3.
Read this again.
http://www.jiskha.com/display.cgi?id=1314169754
To find the density of the glass, we can use the principle of refraction and Snell's law. Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media involved.
In this case, let's assume light is traveling from air to glass and also from air to water.
Using Snell's law for air to glass refraction:
sin(angle of incidence in air) / sin(angle of refraction in glass) = refractive index of air to glass
Using Snell's law for air to water refraction:
sin(angle of incidence in air) / sin(angle of refraction in water) = refractive index of air to water
Because the incidence angle is the same in both cases (it's the same light beam), we can equate the two expressions:
sin(angle of refraction in glass) / sin(angle of refraction in water) = refractive index of air to glass / refractive index of air to water
Now, the refractive indices of air to glass and air to water are given as 1.52 and 1.33 respectively. Plugging in these values:
sin(angle of refraction in glass) / sin(angle of refraction in water) = 1.52 / 1.33
Now, we can use the fact that sin(angle) = 1 / (cosec(angle)) to rewrite:
cosec(angle of refraction in glass) / cosec(angle of refraction in water) = 1.52 / 1.33
Since the refractive indices are greater than 1, we can assume that the angle of refraction is less than 90 degrees, so we can use the cosecant function.
The reciprocal of the sine is the cosecant function, so:
1 / sin(angle of refraction in glass) / 1 / sin(angle of refraction in water) = 1.52 / 1.33
By simplifying, we get:
sin(angle of refraction in water) / sin(angle of refraction in glass) = 1.33 / 1.52
Now, we can find the ratio of the refractive indices in terms of the ratios of the densities of the corresponding media. The refractive index of a medium is inversely proportional to its density, so:
density of air / density of glass = sin(angle of refraction in glass) / sin(angle of refraction in water)
We are given that the density of water is 1 g/cm^3. The density of air is approximately 0.0012 g/cm^3. Substituting these values and the ratio of the refractive indices:
0.0012 / density of glass = 1.52 / 1.33
Simplifying further:
density of glass = (0.0012 * 1.33) / 1.52
Therefore, the density of the glass is approximately 0.001045 g/cm^3.