Planar waves from a monochromatic light source are normally incident on a circular obstacle, which casts a shadow on a screen positioned behind the obstacle. What do the wave properties of light predict about how dark the center of the shadow is?(a) The center of the pattern should be brighter than its surrounding.(b) The center of the pattern should be darker than its surrounding.

correct  is the A

Explanation:

The light is a wave that has travels from two different places, each side of the circular obstacle, so an interference process must be given, which is described by the expression

                a sin θ  = m λ

Where a is the size of the slit, λ the wavelength and m an integer that indicates the order of diffraction.

In the case of the central point, the difference in the optical path of each ray stop is zero, which implies that in some it is also zero, so the waves are in phase for this point and a bright spot must be seen in the center.

When reviewing the answer the correct one is the A

(75°f − 32) × 5/9 = 23.889°c

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.