Physics, 05.08.2020 14:01 destinyd10189

In a Young's double-slit experiment, a set of parallel slits with a separation of 0.102 mm is illuminated by light having a wavelength of 575 nm and the interference pattern observed on a screen 3.50 m from the slits.(a) What is the difference in path lengths from the two slits to the location of a second order bright fringe on the screen?(b) What is the difference in path lengths from the two slits to the location of the second dark fringe on the screen, away from the center of the pattern?

Answers: 3

Show answers

Answers

Answer from: cakey3501

Rounded to three significant figures:

(a) $2 \times 575\; \rm nm = 1150\; \rm nm = 1.15\times 10^{-6}\; \rm m$ .

(b) $\displaystyle \left(1 + \frac{1}{2}\right) \times (575\;\rm nm) \approx 863\; \rm nm = 8.63\times 10^{-7}\; \rm m$ .

Explanation:

Consider a double-slit experiment where a wide beam of monochromatic light arrives at a filter with a double slit. On the other side of the filter, the two slits will appear like two point light sources that are in phase with each other. For each point on the screen, "path" refers to the length of the segment joining that point and each of the two slits. "Path difference" will thus refer to the difference between these two lengths.

Let denote a natural number ( $k \in \left\lbrace0,\, 1,\, 2,\, \dots\right\rbrace$ .) In a double-split experiment of a monochromatic light:

A maximum (a bright fringe) is produced when light from the two slits arrive while they were in-phase. That happens when the path difference is an integer multiple of wavelength. That is: $\text{Path difference} = k\, \lambda$ .Similarly, a minimum (a dark fringe) is produced when light from the two slits arrive out of phase by exactly one-half of the cycle. For example, The first wave would be at peak while the second would be at a crest when they arrive at the screen. That happens when the path difference is an integer multiple of wavelength plus one-half of the wavelength: $\displaystyle \text{Path difference} = \left(k + \frac{1}{2}\right)\cdot \lambda$ .Maxima

The path difference is at a minimum (zero) at the center of the screen between the two slits. That's the position of the first maximum- the central maximum, a bright fringe where k = 0 in $\text{Path difference} = 0$ .

The path difference increases while moving on the screen away from the center. The first order maximum is at k = 1 where $\text{Path difference} = \lambda$ .

Similarly, the second order maximum is at k = 2 where $\text{Path difference} = 2\, \lambda$ . For the light in this question, at the second order maximum: $\text{Path difference} = 2\, \lambda = 2 \times 575\; \rm nm = 1.15\times 10^{-6}\; \rm m$ .

Central maximum: k = 0

, such that $\text{Path difference} = 0$ .First maximum: k = 1

, such that $\text{Path difference} = \lambda$ .Second maximum: k = 2

, such that $\text{Path difference} = 2\, \lambda$ .Minima

The dark fringe closest to the center of the screen is the first minimum. $\displaystyle \text{Path difference} = \left(0 + \frac{1}{2}\right)\cdot \lambda = \frac{1}{2}\, \lambda$ at that point.

Add one wavelength to that path difference gives another dark fringe- the second minimum. $\displaystyle \text{Path difference} = \left(1 + \frac{1}{2}\right)\cdot \lambda$ at that point.

First minimum: k =0

, such that $\displaystyle \text{Path difference} = \frac{1}{2}\, \lambda$ .Second minimum: k =1

, such that $\displaystyle \text{Path difference} = \left(1 + \frac{1}{2}\right)\cdot \lambda$ .

For the light in this question, at the second order minimum: $\displaystyle \text{Path difference} = \left(1 + \frac{1}{2}\right)\cdot \lambda = \left(1 + \frac{1}{2}\right)\times (575\; \rm nm) \approx 8.63\times 10^{-7}\; \rm m$ .

Answer from: Quest

What is the things about?

Answer from: Quest

so here is the information for current research:

-nrel's geothermal analysts, scientists, and engineers perform a full range of research from developing advanced methods of locating and accessing geothermal resources to exploring innovative technologies to extract and produce clean energy from the heat of the earth

and here is the information for the technology of geothermal energy:

-it's clean and sustainable

-resources of geothermal energy range from the shallow ground to hot water and hot rock found a few miles beneath the earth's surface, and down even deeper to the extremely high temperatures of molten rock called magma

-almost everywhere, the shallow ground or upper 10 feet of the earth's surface maintains a nearly constant temperature between 50° and 60°f (10° and 16°c)

-geothermal heat pumps can tap into this resource to heat and cool buildings

-a geothermal heat pump system consists of a heat pump, an air delivery system (ductwork), and a heat exchanger-a system of pipes buried in the shallow ground near the building

-in the winter, the heat pump removes heat from the heat exchanger and pumps it into the indoor air delivery system

-in the summer, the process is reversed, and the heat pump moves heat from the indoor air into the heat exchanger

-the heat removed from the indoor air during the summer can also be used to provide a free source of hot water

Another question on Physics

Physics, 22.06.2019 00:30

Orange juice has a lower or higher viscosity than chocolate syrup

Answers: 2

Answer

Physics, 22.06.2019 09:30

For this car, predict the shape of a graph that shows distance (x) versus time (t). note that time is the independent variable and will be on the bottom axis. need asap

Answers: 1

Answer

Physics, 22.06.2019 14:30

What was the first instrument to ever record an earthquake?

Answers: 1

Answer

Physics, 22.06.2019 21:00

Ascientist wants to test ways to reduce pollution in lake . what is the bestway of doing this

Answers: 2

Answer

You know the right answer?

In a Young's double-slit experiment, a set of parallel slits with a separation of 0.102 mm is illumi...