- Exploring Physics Form 4
- http://physics.tutorvista.com/
- http://www.wikipedia.org/
Sunday 2 October 2011
5.4 Understanding Lenses
~Lenses are divided into
a)convex lens@converging lens@positive lens
b)concave lens@diverging lens@negative lens
-Optical centre, O : A point which all rays traveling through this point pass through the lens in a straight line.
-Principal axis : A straight line which passes through the optical centre , O at a right angles to the plane of the lenses
-Principal focus,F : i) F is a point on the principal axis to which incident rays of light travelling parallel to the principal axis, converge after refraction through a convex lens.
ii) F is a point on the principal axis from which incident rays of light travelling parallel to the principal axis appear to diverge after refraction through a concave lens.
-Object distance, u : Distance of the object from the optical centre,O.
-Image distance, v : Distance of the image from the optical centre,O.
-Focal plane : A plane through the principal focus and parallel to the plane of the lens.
-Focal length, f : Distance between the principal focus, F and the optical centre, O.Focal length = OF.
The focal length of a convex lens is positive whereas the focal length of a concave lens is negative.
★Distant object : u = infinity
★Object distance is more than 2f : u>2f
★Object distance is equal to 2f : u=2f
★Object distance is between f and 2f : f<u<2f
★Object distance is equal to f : u = f
★Object distance is less than f : u<f
★When the object is at infinity
★The image formed is:
-formed at F1
-upright
-diminished
-virtual
★When the object is placed at any position between O and infinity
-upright
-diminished
-virtual
A Laboratory Model of Compound Microscope
The essential parts of a compound microscope are two convex lenses of short focal length. These lenses are referred to as:
The ray diagram given below gives the principle of a compound microscope. The object is mounted on the stand below the microscope tube. The objective lens forms a real, inverted and magnified image (I1) of the object. The image I1 acts as an object for the eye piece. The position of the eyepiece is so adjusted that the image lies within the focus of the eyepiece (Fe). The eyepiece acts like a magnifying glass and forms a virtual erect and magnified image of the object.
Image Formation in a Compound Microscope
Telescope
It consists of two convex lenses called objective and eyepiece. The objective is of large focal length whereas the eyepiece is of short focal length. The distance between the two lenses can be adjusted by adjusting the tube which holds the lens.
The ray diagram showing the principle of the astronomical telescope is given below.
The Differences between Microscope and Telescope
a)convex lens@converging lens@positive lens
-Principal axis : A straight line which passes through the optical centre , O at a right angles to the plane of the lenses
-Principal focus,F : i) F is a point on the principal axis to which incident rays of light travelling parallel to the principal axis, converge after refraction through a convex lens.
ii) F is a point on the principal axis from which incident rays of light travelling parallel to the principal axis appear to diverge after refraction through a concave lens.
-Object distance, u : Distance of the object from the optical centre,O.
-Image distance, v : Distance of the image from the optical centre,O.
-Focal plane : A plane through the principal focus and parallel to the plane of the lens.
-Focal length, f : Distance between the principal focus, F and the optical centre, O.Focal length = OF.
The focal length of a convex lens is positive whereas the focal length of a concave lens is negative.
Power of Lenses
a)Power of lenses,P = 1/f(m) or 100/f(cm)
b)The unit of power of a lens is dioptre,P.
c)The power of a convex lens is taken to be positive.
d)The power of a concave lens is taken to be negative.
Images formed by Convex Lenses
★Distant object : u = infinity
★Image distance : v =f
★Real
★Inverted
★Diminished in size
★On the opposite side of the object
★On the opposite side of the object
★Object distance is more than 2f : u>2f
★Image distance : f<v<2f
★Real
★Inverted
★Diminished in size
★On the opposite of the object
★Diminished in size
★On the opposite of the object
★Object distance is equal to 2f : u=2f
★Image distance : v = 2f
★Real
★Inverted
★Same size as object
★Same size as object
★On the opposite side of the object
★Object distance is between f and 2f : f<u<2f
★Image distance : v>2f
★Real
★Inverted
★Magnified
★On the opposite side of the object
★Object distance is equal to f : u = f
★Images is at infinity
★Virtual
★Upright
★Magnified
★On the same side as the object
★Object distance is less than f : u<f
★Object distance : v>u
★Virtual
★Upright
★Magnified
★On the same side as the object
Images Formed by Concave Lenses
a)Images formed by concave lenses do not depend on the position of the object with respect to the lens.
b)An image formed by a concave lenses is always
i) virtual
ii) upright
iii) diminished
iv) located between the lens and the object
v)the image distance is less than the focal length
★When the object is at infinity
★The image formed is:
-formed at F1
-upright
-diminished
-virtual
★When the object is placed at any position between O and infinity
★The image formed is :
-formed between O and F1-upright
-diminished
-virtual
Linear Magnification
Linear magnification ,
m = Image height / Object height = hI / ho
OR
m= Image distance / Object distance = v / u
Lens Equation
The relationship between distance of the object (u), distance of the image (v) and focal length (f) of the lens is called lens formula or lens equation.
Microscope
 | ||
| Compound Microscope |
The essential parts of a compound microscope are two convex lenses of short focal length. These lenses are referred to as:
- the objective lens or objective
- the eye piece or lens
The ray diagram given below gives the principle of a compound microscope. The object is mounted on the stand below the microscope tube. The objective lens forms a real, inverted and magnified image (I1) of the object. The image I1 acts as an object for the eye piece. The position of the eyepiece is so adjusted that the image lies within the focus of the eyepiece (Fe). The eyepiece acts like a magnifying glass and forms a virtual erect and magnified image of the object.
- The object (O) is placed just outside Fo, the principal focus of the objective lens.
- Fe is the principal focus of the eye lens.
- A real, inverted magnified image I1 is formed. The magnified image I1 acts as an object for the eye lens.
- The final image I2 is virtual and is magnified still further. It is inverted compared with the object. I2 may appear 1000 times larger than the object.
Telescope
 | |
| This type of telescope is used to view heavenly bodies like stars, planets and satellites. |
It consists of two convex lenses called objective and eyepiece. The objective is of large focal length whereas the eyepiece is of short focal length. The distance between the two lenses can be adjusted by adjusting the tube which holds the lens.
The ray diagram showing the principle of the astronomical telescope is given below.
The Differences between Microscope and Telescope
| Compound microscope | Astronomical telescope |
|---|---|
| Objective lens has smaller focal length, than the eyepiece | Objective lens has larger focal length than the eyepiece |
| Distance between the objective lens and the eyepiece is greater than f0+fe | Distance between the objective lens and the eyepiece is equal to f0+fe |
| It is used to see very small objects | It is used to see distant astronomical objects |
5.3 Understanding Total Internal Reflection of Light
When light is incident upon a medium of lesser index of refraction, the ray is bent away from the normal, so the exit angle is greater than the incident angle. Such reflection is commonly called "internal reflection". The exit angle will then approach 90° for some critical incident angle θc , and for incident angles greater than the critical angle there will be total internal reflection.
 |
| Critical Angle |
 |
| Total Internal Reflection |
Calculating the Critical Angle
Now we shall learn how to derive the value of the critical angle for two given media. The process is fairly simple and involves just the use of Snell’s Law that we have already studied.
To recap, Snell’s Law states:
n1 sin θ1 = n2 sin θ2
where n1 is the refractive index of material 1, n2 is the refractive index of material 2, θ1 is the angle of incidence and θ2 is the angle of refraction.
For total internal reflection we know that the angle of incidence is the critical angle.
So,
θ1 = θc.
However, we also know that the angle of refraction at the critical angle is 90◦. So we have:
θ2 = 90◦
We can then write Snell’s Law as:
Now we shall learn how to derive the value of the critical angle for two given media. The process is fairly simple and involves just the use of Snell’s Law that we have already studied.
To recap, Snell’s Law states:
n1 sin θ1 = n2 sin θ2
where n1 is the refractive index of material 1, n2 is the refractive index of material 2, θ1 is the angle of incidence and θ2 is the angle of refraction.
For total internal reflection we know that the angle of incidence is the critical angle.
So,
θ1 = θc.
However, we also know that the angle of refraction at the critical angle is 90◦. So we have:
θ2 = 90◦
We can then write Snell’s Law as:
n1 sin θ1 = n2 sin 90◦
The angle in the medium which causes this is called the critical angle, θc.
If the angle in the medium is greater than the critical angle, then no light is refracted and Total Internal Reflection takes place within the medium.
Critical angle and total internal reflection
When light travels from a medium of high refractive index to one of lower refractive index (e.g. glass into air), it bends away from the normal. If the angle within the medium θm is increased, a point is reached where the angle in θa becomes 90º.The angle in the medium which causes this is called the critical angle, θc.
If the angle in the medium is greater than the critical angle, then no light is refracted and Total Internal Reflection takes place within the medium.
Relationship between critical angle and refractive index
 | |
| At the critical angle, θm = θc and θ a = 90º |
n = 
Effect of a Prism on Light Rays
 |
The rays of light are deflected by 90º |
 |
| The rays of light are inverted.An inverted image is seen. |
 | ||||
The two rays of light are deflected by 180º. The two rays are inverted and an inverted image is seen. |
Phenomenon
 | |
| total internal reflection occurs |
 | |
| total internal reflection occurs |
 | |
| Fish's Eye View |
 |
| Road Mirage |
Application
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| Optical Fibres |
 | |
| Prism Binoculars |
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| Prism Periscope |
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