Physics College

A very thin sheet of brass contains two thin parallel slits. When a laser beam shines on these slits at normal incidence and room temperature (20.0 ∘C ), the first interference dark fringes occur at ± 26.6∘ from the original direction of the laser beam when viewed from some distance. If this sheet is now slowly heated up to 135 ∘C , by how many degrees do these dark fringes change position? Coefficient of linear expansion for brass is α=2.0×10−5(∘C)−1 . Ignore any effects that might occur due to change in the thickness of the slits. (Hint: Since thermal expansion normally produces very small changes in length, you can use differentials to find the change in the angle.)

Answers

Answer 1

We do not know the value of L0 and d, we cannot calculate the exact change in angle. However, we can find the order of magnitude of Δθ by using the values given in the problem.

How solve the problem?

The change in the angle can be calculated by using the formula for linear expansion: ΔL = L0 * α * ΔT, where ΔL is the change in length, L0 is the initial length, α is the coefficient of linear expansion, and ΔT is the change in temperature.

We can assume that the distance between the two slits is the length L0. The change in length ΔL will cause a change in the angle of the dark fringes, which can be calculated using the formula: Δθ = ΔL / d, where Δθ is the change in angle and d is the distance from the slits to the observation point.

So, ΔL = L0 * α * ΔT = L0 * α * (135 - 20)

Δθ = ΔL / d

Substituting the given values, we get:

Δθ = L0 * α * (135 - 20) / d

= L0 * 2.0 x 10^-5 * 115 / d

Since we do not know the value of L0 and d, we cannot calculate the exact change in angle. However, we can find the order of magnitude of Δθ by using the values given in the problem.

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Related Questions

A sprinter with a mass of 70 kg accelerates at a rate of 5 m/s2. What force is the sprinter exerting?

Answers

Answer:

The force exerted by the sprinter can be calculated using Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration:

F = m * a

where:

F is the force

m is the mass of the object (70 kg)

a is the acceleration (5 m/s^2)

Plugging in the values, we get:

F = 70 kg * 5 m/s^2

F = 350 N

So, the sprinter is exerting a force of 350 N. This is the force that the sprinter's legs are applying to the ground, propelling them forward and producing the acceleration.

Starting from a location with position vector 1,=−18.7 m
and 1,=21.5 m
, a rabbit hops around for 10.7
seconds with average velocity ,=−2.17 m/s
and ,=1.71 m/s
. Find the components of the position vector of the rabbit's final location, 2,
and 2,

^ is the same as the picture

Answers

The components of the position vector of the rabbit's final location r₂, x and r₂, y is 36.77 m.

How to calculate position?

To find the final location of the rabbit, calculate the displacement of the rabbit, which is given by the product of average velocity and time.

r₂, x = 1, + vx x t = -18.7 - 2.17 x 10.7 = -43.77 m

r₂, y = 1, + vy x t = 21.5 + 1.71 x 10.7 = 36.77 m

Therefore, the components of the position vector of the rabbit's final location are r2x = -43.77 m and r2y = 36.77 m.

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