A ray in glass is incident onto a water-glass interface, at an angle of incidence equal to half the critical angle for that interface. The indices of refraction for water and the glass are 1.33 and 1.83, respectively. The angle that the refracted ray in the water makes with the normal is closest to:

38°

Explanation:

A

the critical angle can be calculated using expresion below

Sin(θ)critical=nr/ni eqn(1)

θ)critical= critical angle

ni= refractive index of the incident medium= 1.83

nr= refractive index of the refractive medium= 1.33

Substitute the values into eqn (1)

Sin(θ)critical=1.33/1.83

θ)critical=sin-(0.726776)

(θ)critical=46.6168°

From the question, we are told that angle of incidence equals half of the critical angle. This can be expressed as

Angle of incidence = 46.6168°/ 2 = 22.308°

From Snell's law which can be expressed mathematically as

ni × sin(θi = nr × (θr

(θ)i = ngle of incidence 22.308°

(θ)r=the angle of refraction

nr = refractive index of the refraction medium of that of water,1.33

nr is the refractive index of the incidence medium of that of glass, 1.43

Then if we substitute we have

1.83 × sin(23.304)= 1.33 × sin (θr

Sin (θr=[ 1.83×sin(23.304)]/1.33

sinθr=0.54434

Sin-1(0.54434)

θr=32.98°

Hence, The angle that the refracted ray in the water makes with the normal is closest to is 32.98°

d. learned preferences i believe is your answer

quantum mechanics or quantum physics is physics of very small objects (particles) and physical entities.

quantum physics has some parallels to our macro world and some pretty unique ideas which theoretically and mathematically proven to be true even though we will never be able to access them because of our size.

there are many types of particles: subatomic, elementary etc.

subatomic means they are smaller than atom, elementary means they are at the very basis of everything.

subatomic particles are for eg. protons, neutrons but not electrons.

elementary particles are categorised into 3 groups by what they do.

these 3 groups are quarks, leptons and bosons.

light for example is a particle more precisely a photon a part of leptons.

proton (subatomic particle) is made out of 2 up quarks and 1 down quark each of these has a fractional charge like . (i crazy)

most famous scientist who contributed to this physics are:

the topic itself us understand a lot and will probably be vastly used in the future (quantum computers, understanding the big bang,

we also must not forget quantum effects like:

and there is more. but probably too much for this answer to be consistent due to my average understanding of this topic.

hope this you understand quantum mechanics a little more. i'm not an expert in the topic (so don't be like wth if you are an expert) but i'm very interested in it.

anyways quantum physics is a very hard topic (harder than physics (perhaps)) therefore searching for every information there is about it and learning it is unfortunately impossible (you can only specialise into 1 - 3 things or more (perhaps

have fun and i wish you luck!

r3t40