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kaheart [24]
3 years ago
11

A slit 0.240mm wide is illuminated by parallel light rays with a wavelength 600nm . The diffraction pattern is observed on a scr

een that is 3.50m from the slit. The intensity at the center of the central maximum (theta = 0) is 4.10�10?6 W/m^2. What is the distance on the screen from the center of the central maximum to the first minimum? What is the intensity at a point on the screen midway between the center of the central maximum and the first minimum?Expert Answer
Physics
1 answer:
taurus [48]3 years ago
3 0

To solve this exercise, it is necessary to apply the concepts on the principle of superposition, specifically on constructive interference,

Constructive interference (light spot) is defined by

dsin\theta=m\lambda

Where,

m = The integer m is called the interference order and is the number of wavelengths by which the two paths differ.

\lambda = wavelenght

d = Distance

For smaller angles sin\theta = tan\theta,

d tan\theta = m \lambda

From the trigonometric properties it is understood that so the is - in this case - the length measured vertically by reason of distance, that is

d*\frac{y}{L} = m\lambda

Re-arrange to find y,

y = \frac{m\lambda L}{d}

Replacing our values

y  = \frac{(1)(600*10^{-9}(3.5m)}{0.240*10^{-3}m}

y = 8.75*10^{-3}m

y = 8.75mm

PART B) To calculate the intensity it is necessary to find the angle between the previously calculated height and distance in order to calculate the phase angle, in other words,

tan\theta' = \frac{y}{L}

tan\theta' = \frac{1/2(8.75*10^{-3})}{3.5}

\tetha = 0.07161\°

Therefore phase angle is

\gamma = \frac{2\pi}{\lambda}sin\theta'

\gamma = \pi

The intensity formula would then be given by,

I = I_0 \frac{sin\frac{\gamma}{2}^2}{\frac{\gamma}{2}}

I = 4.1*10^{-6}(\frac{4}{\pi})

I = 1.66*10^{-6}W/m^2

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uniform disk with mass 40.0 kg and radius 0.200 m is pivoted at its center about a horizontal, frictionless axle that is station
Alex787 [66]

Answer:

The magnitude of the tangential velocity is v= 0.868 m/s

The magnitude of the resultant acceleration at that point is  a = 4.057 m/s^2

Explanation:

From the question we are told that

      The mass of the uniform disk is m_d = 40.0kg

       The radius of the uniform disk is R_d = 0.200m

       The force applied on the disk is F_d = 30.0N

Generally the angular speed i mathematically represented as

             w = \sqrt{2 \alpha  \theta}

Where \theta is the angular displacement given from the question as

           \theta  = 0.2000 rev = 0.2000 rev * \frac{2 \pi \ rad }{1 rev}

                 =1.257\  rad

   \alpha is the angular acceleration which is mathematically represented as

                    \alpha = \frac{torque }{moment \ of  \ inertia}  = \frac{F_d * R_d}{I}

    The moment of inertial is mathematically represented as

                     I = \frac{1}{2} m_dR^2_d

Substituting values

                    I = 0.5 * 40 * 0.200^2

                        = 0.8kg \cdot m^2

Considering the equation for angular acceleration

               \alpha = \frac{torque }{moment \ of  \ inertia}  = \frac{F_d * R_d}{I}

Substituting values

               \alph\alpha = \frac{(30.0)(0.200)}{0.8}

                   = 7.5 rad/s^2

Considering the equation for angular velocity

    w = \sqrt{2 \alpha  \theta}

Substituting values

     w =\sqrt{2 * (7.5) * 1.257}

         = 4.34 \ rad/s

The tangential velocity of a given point on the rim is mathematically represented as

                 v = R_d w

Substituting values

                    = (0.200)(4.34)

                     v= 0.868 m/s

The radial acceleration at hat point  is mathematically represented as

            \alpha_r = \frac{v^2}{R}

                  = \frac{0.868^2}{0.200^2}

                 = 3.7699 \ m/s^2

The tangential acceleration at that point is mathematically represented as

               \alpha _t = R \alpha

Substituting values

           \alpha _t = (0.200) (7.5)

                 = 1.5 m/s^2

The magnitude of resultant acceleration at that point is

                 a = \sqrt{\alpha_r ^2+ \alpha_t^2 }

Substituting values

                a = \sqrt{(3.7699)^2 + (1.5)^2}

                   a = 4.057 m/s^2

         

7 0
3 years ago
A charge q1 of -5.00 x 10^-9 C and a charge q2 of -2.00x 10^-9 C are separated by a distance of 40.0 cm. Find the equilibrium po
aleksandrvk [35]

Answer:

Explanation:

Let the equilibrium position of third charge be x distance from q₁.

Force on third charge due to q₁

= 9 x 10⁹ x 5 x 10⁻⁹ x 15 x 10⁺⁹ / x²

Force on third charge due to q₂

= 9 x 10⁹ x 2 x 10⁻⁹ x 15 x 10⁺⁹ /( .40-x)²

Both the force will act in opposite direction and for balancing , they should be equal.

9 x 10⁹ x 5 x 10⁻⁹ x 15 x 10⁺⁹ / x² = 9 x 10⁹ x 2 x 10⁻⁹ x 15 x 10⁺⁹ /( .40-x)²

5  / x² = 2 / ( .4 - x )²

Taking square root on both sides

2.236 / x = 1.414 / .4 - x

2.236 ( .4 - x ) = 1.414 x

.8944 - 2.236 x = 1.414 x

.8944 = 3.65 x

x = .245 m

24.5 cm

So the third charge should be at a distance of 24.5 cm from q₁ .

4 0
2 years ago
What is the 5 quantitative research problems?<br>​
iogann1982 [59]

Answer:

There are four main types of Quantitative research: Descriptive, Correlational, Causal-Comparative/Quasi-Experimental, and Experimental Research. attempts to establish cause- effect relationships among the variables. These types of design are very similar to true experiments, but with some key differences.

Explanation:

Quantitative research is defined as a systematic investigation of phenomena by gathering quantifiable data and performing statistical, mathematical, or computational techniques.

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7 0
2 years ago
Which property does not apply to a motor? A. It uses an electromagnet. B. The direction of current changes twice during the rota
Rufina [12.5K]

Answer:  

     

Explanation:

A motor converts electrical energy to mechanical energy. A current carrying coil is placed between electromagnets. A magnetic force is exerted on the coil which makes it rotate. The direction of current changes twice during the rotation of the coil. An outside source of electric current is used.

Thus, the wrong statement is D. It converts mechanical energy into electrical energy. It is the generator which converts mechanical energy into electrical energy.

3 0
3 years ago
Read 2 more answers
1. The geologic time scale divides time into years and centuries, true or false
hodyreva [135]

Answer:

The answer is "False"

Explanation:

The geologic time scale is the "schedule" for occasions in Earth history. It partitions time into named units of unique time called in descending order of duration "eons, eras, periods, epochs, and ages". The specification of those geologic time units depends on stratigraphy, which is the relationship and order of rock layers. The fossil structures that happen in the stones, nonetheless, give the central methods for setting up a geologic time scale, with the circumstance of the development and vanishing of far and wide species from the fossil record being used to outline the beginnings and endings of ages,, periods, and different stretches.

Geologic time is the broad time period involved by the geologic history of Earth. Formal geologic time starts toward the beginning of the Archean Eon (4.0 billion to 2.5 billion years back) and proceeds to the current day.

5 0
3 years ago
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