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desmond iking
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Homework Statement
i am confused which eqaution to use for formula of refraction at spherical surface , do i need to put a modulus for n2-n1 ? some book gives modulus , while the other book not . which one is correct?
ehild said:See http://www.tutorvista.com/content/physics/physics-iv/optics/refracting-surface.php
You need n2-n1 on the right-hand side.
ehild
ehild said:I might have misunderstood you. What do you mean on "modulus"? Absolute value?
Check the sign convention of R and that of the image distance before using the formula. It might differ from book to book.
ehild
ehild said:The solution uses the formula ##\frac{n_1}{u}+\frac{n_2}{v}=\frac{n_2-n_1}{R}## (this is more common than the one you used) with the sign convention: R is positive if the spherical surface is convex as viewed by the incoming ray. R is negative if the surface is concave from the direction the light arrives. The image distance u is positive if the image is at that opposite from where the light arrives, and negative if it is at the same side. The object distance is positive if it is in front of the surface, ( at that side from where the light arrives).
The sign convention in case of the formula you cited is that the distances to the left from the surface are negative and they are positive if they are to the right of the surface. In that case u would be -30 cm.
In case of the problem you show, R is negative, R=-20 cm. n1=1, n2=1.5, n2-n1=0.5. If you calculate the image distance with the formula ##\frac{n_1}{u}+\frac{n_2}{v}=\frac{n_2-n_1}{R}##, ##\frac{1}{u}+\frac{1.5}{v}=\frac{0.5}{-20}## you get the result in the book.
Using your previous formula, both the object and the centre of the sphere are to the left from the refracting surface, so both u and R are negative. u=-30 cm, R=-20 cm, so you get ##\frac{1.5}{v}-\frac{1}{-30}=\frac{0.5}{-20}## which gives the same result.
Do not put absolute value anywhere.
ehild
ehild said:The solution uses the formula ##\frac{n_1}{u}+\frac{n_2}{v}=\frac{n_2-n_1}{R}## (this is more common than the one you used) with the sign convention: R is positive if the spherical surface is convex as viewed by the incoming ray. R is negative if the surface is concave from the direction the light arrives. The image distance u is positive if the image is at that opposite from where the light arrives, and negative if it is at the same side. The object distance is positive if it is in front of the surface, ( at that side from where the light arrives).
The sign convention in case of the formula you cited is that the distances to the left from the surface are negative and they are positive if they are to the right of the surface. In that case u would be -30 cm.
In case of the problem you show, R is negative, R=-20 cm. n1=1, n2=1.5, n2-n1=0.5. If you calculate the image distance with the formula ##\frac{n_1}{u}+\frac{n_2}{v}=\frac{n_2-n_1}{R}##, ##\frac{1}{u}+\frac{1.5}{v}=\frac{0.5}{-20}## you get the result in the book.
Using your previous formula, both the object and the centre of the sphere are to the left from the refracting surface, so both u and R are negative. u=-30 cm, R=-20 cm, so you get ##\frac{1.5}{v}-\frac{1}{-30}=\frac{0.5}{-20}## which gives the same result.
Do not put absolute value anywhere.
ehild
desmond iking said:i still can't understand why the u is -30cm. the light ray passed from left to right, (the object is placed to the left of the refracting surface) , so the object is REAL am i right? so it should be POSITIVE ?
desmond iking said:here's another case . now , the n2-n1 is negative where 1-1.5 = -0.5
if i put modulus on it , my n2-n1 is always positive , but the book didnt put modulus on it. here's a better case showing whether the n2-n1 should be placed modulus or not.
The formula for refraction at a spherical surface is: n1(sinθ1)/n2(sinθ2) = (R - d)/R, where n1 is the refractive index of the initial medium, n2 is the refractive index of the final medium, θ1 is the angle of incidence, θ2 is the angle of refraction, R is the radius of curvature of the spherical surface, and d is the distance between the point of incidence and the center of curvature.
The refractive index of a medium is calculated by dividing the speed of light in a vacuum by the speed of light in the medium. It is represented by the symbol n and is a dimensionless quantity.
The angle of incidence is the angle between the incident ray and the normal line at the point of incidence, while the angle of refraction is the angle between the refracted ray and the normal line at the point of incidence. The two angles are related by Snell's Law: n1(sinθ1) = n2(sinθ2).
The radius of curvature, represented by the symbol R, is the distance between the center of curvature and the point of incidence on the spherical surface. It determines the curvature of the surface and affects the amount of refraction that occurs. A larger radius of curvature leads to less refraction, while a smaller radius of curvature leads to more refraction.
The formula for refraction at a spherical surface is used in many real-life applications, such as in eyeglasses and contact lenses, lenses in cameras and telescopes, and curved mirrors in solar panels and telescopes. It also helps in understanding the behavior of light in different mediums and predicting the path of light rays through lenses and other optical instruments.