Ray Optics and Optical Instruments

Ray Optics and Optical Instruments

Ray Optics is a very commonly heard term,as it is related to light which is a very important part of our daily life.Optics is the branch of physics which studies the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it.Ray optics is also called geometrical optics as it uses the geometry of straight-line paths (rays) to explain the optical phenomena. Optics usually describes the behavior of visible, ultraviolet, and infrared light.Ray optics, infact, is the limiting case of wave optics. This means for most practical purposes, we can ignore the deviation from straight-line path as postulated by wave theory.

Optical Instruments: Let us learn about some of the optical Instruments
The first thing that comes to our mind when we say "Optical instruments" is a pair of spectacles.......but it is not true they are other types of optical instruments too,let us learn about the formation of various types of images by a lens for different positions of the object.

Microscopes:

A microscope is an optical device which produces a highly magnified image of very small object such as micro-organisms. Based on the design, there are two types of microscopes. They are, simple microscope and compound microscopes.
Simple Microscope

A simple microscope is nothing but a single biconvex lens. It is referred to as magnifying glass.
Compound Microscope

A compound microscope is an optical instrument which is used to magnify very small objects like blood cells, bacteria which otherwise cannot be seen with the naked eye.
Telescopes

Telescope is an optical instrument which is used for viewing heavenly bodies and distant objects.
Astronomical Telescope

This type of telescope is used to view heavenly bodies like stars, planets and satellites.

We might also come across questions such as:Which instrument is used to measure temperature??

The answer would be a "Thermometer". These are some basic examples of Optical Instruments.


Hope you like the above example of Ray Optics and Optical Instruments
Please leave your comments, if you have any doubts.

Standard Deviation word problem in Probability Theory

In probability theory and statistics, the standard deviation of a statistical population, a data set, or a probability distribution is the square root of its variance. standard deviation formula is a widely used measure of the variability or dispersion, being algebraically more tractable though practically less robust than the expected deviation or average absolute deviation.We can use Standard deviation calculator to make it easy.

In simple terms, it shows how much variation there is from the "average" (mean). It may be thought of as the average difference of the scores from the mean of distribution, how far they are away from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.Let's see an example from probability problems
Question

A volunteer ambulance service handles 0 to 5 service calls on any given day .The probability distribution for the number of service calls is as follows :

Number of calls : 0 probability 0.08,1-0.16,2-0.27,3-0.20,4-0.15and 5-0.14

a)What is the expected number of service calls(2 decimals)?

b)What is the variance in the number of service calls(to 2 decimals)?

c)What is the standard deviation (to 2 decimals)?

Answer

a)

Expected number= 0(0.08)+1(0.16)+2(0.27)+3(0.20)+4(0.15)+5(0.14)

=0+0.16+0.54+0.60+0.60+0.70

=2.6


b)

Var(x) = E(x²)-[E(x)]²

=8.94-(2.60)²

=8.94+6.76

=2.18

c)

Standard deviation = v2.18 = 1.48

How to solve a inequality

An inequality is a statement about the relative size or order of two objects, or about whether they are the same or not (See also: equality).these points covered when linear equations explained

• The notation a < b means that a is less than b.
• The notation a > b means that a is greater than b.
• The notation a ≠ b means that a is not equal to b, but does not say that one is greater than the other or even that they can be compared in size.

In each statement above, a is not equal to b. These relations are known as strict inequalities. Let's see an example on this from 9th grade math

Question:-

Solve the inequality

13 ≤ 3y+4 < style="font-weight: bold; color: rgb(51, 51, 255);">

Answer:-


We have to find the range of y.

So we isolate y.

13-4 ≤ 3y+4-4 < 18-4

9 ≤ 3y < 14

Noe divide each term by 3.

we get 3 ≤ y < 14/3 is the answer

similarly we can get more free answers to math problems

Problem on Distance Formula

The distance formula can be obtained by creating a triangle and using the Pythagorean Theorem to find the length of the hypotenuse. The hypotenuse of the triangle will be the distance between the two points.

Lets see an example on this from college algebra tutorial


Find the distance between(-3,-2)and (1,7)

here we have

x1=-3 ,y1=-2 and x2=1 and y2=7


We know the distance formula

D= √(x₂-x₁)²+(y₂-y₁)²

x₂ and y₂ are the x,y coordinates for one point
x₁and y₁ are the x,y coordinates for the second point
d is the distance between the two points
one of the Discrete math Tutor is solving the above problem here

D =√(-3-1)²+(-2-7)²

= √ (-4)² +(-9)²

= √ 16 + 81

= 9.848

So the distance is 9.85 approximately

Question on Calculating Simple Interest

In simple term the word Simple Interest refers just the amount of money paid on a loan. It's the easiest type of interest or most basic type of interest. In order to understand how various types of transactions work, it helps to have a complete understand the terms used.

For example: you may pay interest on a car loan, and it is very much necessary and important to understand how interest works. Better yet, your bank may be paying you interest on your deposits – and you can maximize your earnings by knowing more about interest.

Here S.I refers to simple interest.
Formula for S.I =

P x T x R
  100

Question: If 11,000,00 dollars is invested. Part of the 11,000,00 is invested 4% and the rest at 7%.
If the investment earns $888.00 per year,how much was invested at each rate?

Answer :

Principal time rate of interest simple interest earned
   x      1            4%              0.04x
1000-x    1            7%             .07(11000-x)

Simple interest = PTR
Where P is the Principal. T is the time and R is the rate of interest
SI = 680
Therefore

0.04x + 0.07(11000-x) = 680
0.04x + 770 - 0.07x   = 680

     -0.03x + 770   = 680
     -0.03x         = 680 - 770
     ------           ----------  
     -0.03            -0.03
          x         = 90/0.03
          x         = 3,000

x = 3,000
so, 3,000 is invested at 4% and 8,000 is the principal invested at 7%

A problem on Logarithms

Topic:-Logarithms

The logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce the number.
For example, the logarithm of 1000 to the base 10 is 3, because 3 is how many 10s you must multiply to get 1000: thus 10 × 10 × 10 = 1000; the base 2 logarithm of 32 is 5 because 5 is how many 2s one must multiply to get 32: thus 2 × 2 × 2 × 2 × 2 = 32. In the language of exponents: 10³ = 1000, so log₁₀1000 = 3, and 2⁵ = 32, so log₂32 = 5.
Let's see a problem on logarithms.

Question:-

solve 6^x+5=3^x-4

Answer:-

Given 6x+5=3x-4

log 6 x+5=log 3x-4

(x+5)log6 = (x-4)log3

xlog6+5log6 = xlog3-4log3

xlog6-xlog3= -4 log3-5log6

x[log6-log3]= -[4log3+5log6]

xlog 6/2 = -[log 34+log65]

xlog3= -log34*65

     -log(34*65)
x=  -----------------
       log3

x=-log3(34*65)

For more help on this ,you can reply me.

problem on logarithms

Topic:-logarithms

To solve logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce the number.
Example logarithm problems : 1000 to the base 10 is 3, because 3 is how many 10s you must multiply to get 1000: thus 10 × 10 × 10 = 1000; the base 2 logarithm of 32 is 5 because 5 is how many 2s one must multiply to get 32: thus 2 × 2 × 2 × 2 × 2 = 32. In the language of exponents: 10³ = 1000, so log₁₀1000 = 3, and 2⁵ = 32, so log₂32 = 5.
The logarithm of x to the base b is written log_b(x) or, if the base is implicit, as log(x). So, for a number x, a base b and an exponent y,

An important feature of logarithms is that they reduce multiplication to addition, by the formula:

This math help is having a example

Question:-

         y        
solve log2---- = 4          
         3

Answer:-

         y        
here  log2---- = 4          
         3

log rule:-

logba = x

bx=a

So,We get
             y
   24= ---
             3

            y
  2*2*2*2= ---
            3
           y
     16 = ---
           3

    16*3=y

    So y=48 is the Answer.

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