(1) For AB = 20 cm, a narrow parallel beam entering from left side will come out from other side as a parallel beam.
To determine the correct statement, we need to analyze the given situation.
The capsule-shaped glass consists of a hemispherical portion on the sides and a cylindrical portion in between. The radius of curvature for the spherical portion is given as 10 cm.
Let's analyze each statement:
(a) For ab = 20 cm, a narrow parallel beam entering from the left side will come out from the other side as a parallel beam.
This statement is true. When the narrow parallel beam enters the glass at point a and passes through the spherical portion, it will refract according to Snell's law. However, since the radius of curvature for the spherical portion is equal on both sides, the beam will emerge parallel to its original direction.
(b) For ab = 20 cm, and surrounding air being replaced by a medium, u = 3/2, on both sides, light will come out as a diverging beam.
This statement is false. If the surrounding medium has a refractive index of u = 3/2 on both sides, the light will still undergo refraction at the spherical portion of the glass. However, due to the symmetrical shape and equal radius of curvature on both sides, the light will emerge parallel to its original direction, not as a diverging beam.
(c) For ab = 20 cm, and surrounding air being replaced by a medium, μ = 3/2, on both sides, light will come out as a parallel beam.
This statement is false. The refractive index given as μ = 3/2 does not match the refractive index of the glass, which is given as μ = 2. Therefore, the light will not emerge as a parallel beam.
(d) For the surrounding medium with u = 3/2, if the emergent beam has to be parallel, then ab has to be bigger than 20 cm.
This statement is false. The emergent beam will be parallel regardless of the value of ab. The parallel nature of the beam is determined by the symmetrical shape and equal radius of curvature of the spherical portion of the glass.
Therefore, the correct statement is (a) for ab = 20 cm, a narrow parallel beam entering from the left side will come out from the other side as a parallel beam.
