**Determining the Diameter of the Central Bright Area in Light Diffraction****Problem Statement:**Light of wavelength 427 nm illuminates a round 0.2-mm diameter hole. A screen is placed 7.6 m behind the slit. What is the diameter of the central bright area on the screen in millimeters? Give the answer with no decimal places please.**Explanation:**When light of a specific wavelength passes through a small circular opening, it diffracts and forms a pattern on the screen. In this scenario, we have:- **Wavelength (\(\lambda\))**: 427 nm (nanometers)- **Diameter of the hole**: 0.2 mm (millimeters)- **Distance from the hole to the screen (\(L\))**: 7.6 m (meters)Using the formula for the diameter of the first diffraction minimum (central bright area) in the Fraunhofer diffraction pattern for a circular aperture:\[ d = 2.44 \times \frac{\lambda L}{D} \]Where:- \(d\) is the diameter of the central bright area,- \(\lambda\) is the wavelength of light,- \(L\) is the distance from the hole to the screen,- \(D\) is the diameter of the hole.First, let's convert the wavelength into millimeters to be consistent:\[ \lambda = 427 \, \text{nm} = 427 \times 10^{-6} \, \text{mm} \]Plug these values into the formula to find \(d\):\[ d = 2.44 \times \frac{427 \times 10^{-6} \times 7.6}{0.2} \]Calculate the value of \(d\):\[ d = 2.44 \times \frac{3245.2 \times 10^{-6}}{0.2} \]\[ d = 2.44 \times 16226 \times 10^{-6} \]\[ d = 2.44 \times 16.226 \]\[ d \approx 39.6 \, \text{mm} \]Rounding to the nearest whole number:\[ \boxed{40 \, \text{mm}} \]Therefore, the diameter of the central bright area on the screen is approximately **40 millimeters**.

Given wavelength (λ)=427 nm hole diameter (d)=0.2 mm distance of screen (D)=7.6 m Required diameter…

Light of wavelength 427 nm illuminates a round 0.2-mm diameter hole. A screen is placed 7.6 m behind the slit. What is the diameter of the central bright area on the screen in millimeters? Give the answer with no decimal places please.

Light of wavelength 427 nm illuminates a round 0.2-mm diameter hole. A screen is placed 7.6 m behind the slit. What is the diameter of the central bright area on the screen in millimeters? Give the answer with no decimal places please.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

Light of wavelength 0.616 um passed through two slits separated by distance d=2.61 µm and creates an interference pattern that can be observed on a screen placed distance 0.86 m away. The bright fringes in the pattern are not equidistant. What is the distance between fırst and third bright band observed on the screen? Provide your answer in centimeters, with a precision one place after decimal.
A laser light source with wavelength λ = 545 nm is incident on a diffraction grating (as in the figure). The grating has 495 slits per mm. An observation screen is a distance L = 0.35 m from the grating. What is the separation between individual slits in the grating? Be careful with units: 1 nm = 10-9 m, 1 mm = 10-3 m, and 1 cm = 10-2 m. d = nm What is the distance y along the screen where the first-order diffraction peak is observed? y= cm source grating m=1
Problem 2: Consider light that has its third minimum at an angle of 23.6° when it falls on a single slit of width 3.55 μm. Randomized Variables 9 = 23.6° w = 3.55 um D Find the wavelength of the light in nanometers. λ=1 sin() cos() cotan() asin() atan() acotan() tanh() cosh() O Degrees Hints: 2% deduction per hint. Hints remaining: 2 Submit tan() JU acos() E sinh() cotanh() Radians Hint ( + 7 8 9 4 5 6 1 0 VO BACKSPACE Feedback 2 3 All content © 2022 Expert TA, LLC DEL HOME END I give up! Feedback: 2% deduction per feedback. CLEAR
Light with wavelength 2 passes through a narrow slit of width w and is seen on a screen which is located at a distance D in front of the slit. The first minimum of the diffraction pattern is at distance d from the middle of the central maximum. Calculate the wavelength of light if D=2.4 m, d =1 mm and w = VAD.Give your answer in nanometers. Answer: Choose...
Light with a wavelength of 418 nm goes trough a slilt that is 65 micrometers wide and falls on a screen that is 30 m away. What is the full width of the central bright spot of the diffraction pattern? Please give your answer in meters. You may use the small angle approximation.