1. The refractive index n of glass depends on the color (wavelength) of the ligh

Question

1. The refractive index n of glass depends on the color (wavelength) of the light passing through it. The most common optical glass, Borosilicate BK7, is characterized at wavelength 486.1 nm (blue, designated with letter F) -> nF=1.52238, and at wavelength 656.3 nm (red, designated with letter C) -> nC=1.51432. Two beams (one of each wavelength) are prepared to coincide, and enter the flat polished surface of a BK7 block at angle of 45 arc degree measured from the normal to the surface. What is the angle between the blue beam and the red beam in the glass block?

2. What will be the distance between the lens and the image if the object is placed at the focal distance from the lens?

Explanation / Answer

(1)     We can use the Law of Refraction (ie, Snell's Law) to separately find the angle of refraction for the blue and red light .

The angle of incidence for both colors of light is given to be 45 deg. The problem does not specify whether the first medium is air or a vacuum, but I will assume it is a vacuum and use n1 = 1.0 exactly.

For BLUE, the setup is   (1.0) sin 45 = (1.52238) sin theta.      This gives the angle of refraction for BLUE to be: theta = 27.6762deg

For RED, the setup is   (1.0) sin 45 = (1.51432) sin theta.      This gives the angle of refraction for RED to be: theta = 27.8363 deg

However, the problem does NOT ask for either of these angles, but wants the angle BETWEEN the blue and red beams, which is found by simply subtracting the above two angles to get a final answer of     delta theta = 0.160084 deg.

(2) There are two ways to answer this. If you construct or look up the ray diagram when an object is placed exactly 1 focal length f from the lens, you will find that the image is located at infinity on the other side of the lens. Thus, the distance between the lens and the image is infinite.

You can also obtain this same answer by using the lens eqn:    1 / do + 1 / di = 1 / f   where it is given that the object distance

do = f.   Pluggin in this fact gives:     1 / f + 1 / di = 1 / f   .   Now the 1 / f   terms cancel out on each side and we are left with

                    1 / di = 0 .    This means that di = infinity.   

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.