Question

explain nature of a particle b particle in photographic plate..... ​

Answer 1

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The thickness of the trace of a light beam which activates a photographic plate is finite, and this is a restriction, therefore, on the interpretation of an image. The hair-line of a measuring instrument, the interval between two definite marks, the breadth of the needle of a galvanometer, all lead to inaccuracy in measurement. The stability of an oscillator is limited to a certain value. If a quartz oscillator, accurate to one part in 104, is employed in an oscillator circuit, the accuracy of the frequency f provided will be one part in 104, which means that the error so far as frequency is concerned is f parts in 104. In electronic circuitry, such elements as resistors and capacitors are employed, and the values of these are usually only accurate to within 5 or 10 per cent.

Calibration errors are very serious, since they have repercussions along the whole measuring chain.

It has already been seen that the error due to quantization is less than or equal to the distance between two levels of quantization. We shall now examine the interpolation error introduced when a true curve is represented by a succession of horizontal steps.

Let g(t) be the real continuous function, for which the discontinuous function f(t) is substituted. At any instant, the error introduced is

ε(t)=g(t)−f(t).

If Δt is the sampling interval: t1 = Δt, t2 = 2Δt, … tn = nΔt, …, and

ε1(t)=g(t)−g(0)for0<t<t1ε3(t)=g(t)−g(t2)for

The root mean square error, therefore, is given by

ε2¯=∫ot1ε12(t)dt+∫t1t3ε32(t)dt+…=∫ot1[g(t

The mean error is

εmean=1nΔt[∫onΔt[g(t)−f(t)]dt]nΔt→∞=[g(t

It is sometimes easy to calculate g(t) if this is a simple function, but usually it fluctuates in a random manner; it is then necessary to proceed graphically.

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Answer 2

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• The thickness of the trace of a light beam which activates a photographic plate is finite, and this is a restriction, therefore, on the interpretation of an image.

• The hair-line of a measuring instrument, the interval between two definite marks, the breadth of the needle of a galvanometer, all lead to inaccuracy in measurement.

• The stability of an oscillator is limited to a certain value. If a quartz oscillator, accurate to one part in 104, is employed in an oscillator circuit, the accuracy of the frequency f provided will be one part in 104, which means that the error so far as frequency is concerned is f parts in 104.

• In electronic circuitry, such elements as resistors and capacitors are employed, and the values of these are usually only accurate to within 5 or 10%.

• Calibration errors are very serious, since they have repercussions along the whole measuring chain.

• It has already been seen that the error due to quantization is less than or equal to the distance between two levels of quantization. We shall now examine the interpolation error introduced when a true curve is represented by a succession of horizontal steps.

Let g(t) be the real continuous function, for which the discontinuous function f(t) is substituted. At any instant, the error introduced is :

1. ε(t) = g(t)− f(t).
2. If Δt is the sampling interval: t1 = Δt, t2 = 2Δt, … tn = nΔt, …, and
3. ε1(t)= g(t) −g(0) for 0 <t< t1ε3(t)= g(t) −g(t2) for The root mean square error, therefore, is given by :
4. ε2¯=∫ot1ε12(t)dt +∫t1t3ε32(t)dt+…= ∫ot1[g(t
5. The mean error is εmean=1nΔt[∫onΔt[g(t) −f(t)]dt]nΔt→∞= [g(t

It is sometimes easy to calculate g(t) if this is a simple function, but usually it fluctuates in a random manner; it is then necessary to proceed graphically.