OBJECTIVE: To find the refractive indexes of (a)water (b) oil using a plane mirror, an equiconvex lens, and an adjustable object needle.
APPARATUS: A convex lens of focal length 20cm, a plane mirror, mirror, given liquid (say water),oil, water),oil, clamp stand, plumb line, knitting needle, meter scale, cork, a spherometer.
DIAGRAM:
Fig: Focal length of glass convex lens and liquid lens combination
THEORY: 1. If f1 and f2 be the focal length of the glass
convex lens and liquid lens and f be the focal length of their combination then:-
2.Liquid lens formed a plano-concave lens with R1 = R and R2 = ∞ then by using lens maker's formula
1 f 2
= (μ − 1) ⌊ R1 − R1 ⌋ 1 2 = (μ
1 − 1) ⌊ R1
−
1 = ( μ -1 ) ⌊ R − 0⌋ 1 f 2
=
(μ−1) R
1 ⌋ ∞
R μ = f +1 2
Where n=Refractive index of the liquid R=The radius of the curvature of the convex lens.
3.The radius of the lower surface of the convex lens is given by: 2
l R= 6h
+
h 2
Here, l is the average distance between the legs of the spherometer and h is the difference in the reading of the spherometer when placed first on the convex lens and then on plane mirror.
PROCEDURE: A : For focal length of convex lens: 1) At the plane base of iron stand , place the plane mirror horizontally with its reflecting surface facing upwards. 2) clamp the needle horizontally on the stand by passing it through the cork.Adjust its position in such a manner that the tip of needle lies along the principal axis, in the line with optical center of the lens 3) let height of needle be slightly greater than the focal length of the lens 4) observe the image of the needle in the lens form above.coincide the tip of needle ands its image by adjusting
its position along the stand .make fine adjustments to remove any parallax if present. 5)measure the distance between tip of needle and (i) upper surface of the lens (fu ),(ii) lower the surface of lens (f1 ).find the mean value ofg f =
f u+ f 1 2
.This is the focal length of
convex lens 6) take at least four set of readings and find the mean value of focal length 7) Pour a few drops of water in the plane mirror to form a thin layer over it .this forms a plano concave(water)lens between mirror surface and convex lens. agin follow the same procedure to find the focal length of this combination of water lens and convex lens
B : For radius of curvature of convex lens surface: 8) Find the pitch and at least count of given spherometer wip the convex lens dry and place the spherometer on the lens.
9) Lower down the screw of spherometer till its tip just touches the lens,Record the reading the circular scale 10) Now place the spherometer on the plane mirror surface(after reducing the lens).Again lower down the screw till its tip touches the mirror surface.Again record the circular scale reading.The difference between these two readings gives the value of sagitta(h) 11) find 2-3 values of ‘h’ and calculate its mean value. 12) to find the value of ‘I, i.e, the distance between legs of spherometer, press it on page of your notebook.The impressions of tips of legs will be formed.join these points using a sharp pencil pencil.Measure the distance between them and find the mean value of ‘I”
OBSERVATIONS:
Distance of Tip of needle from Upper surface of lens fu(cm)
Plane Mirror feu(cm)
Mean Value
f1 =
Mean Value of focal length
f u+ f l 2
Only Convex lens on plane mirror
9.5
10.1
9.8
With liquid in between plane mirror and convex lens
14.1
15
14.55 f =14.55 cm
With oil
17.4
18.2
17.8
Position of spherometer
Pitch scale reading(PSR)
circular scale reading(CSR)
On the plane mirror
1 mm
24
On the convex lens
0 mm
5
f1= 9.8 cm
f = 17.8 cm
D=PSR+CSR(LC) a = 0.124 cm b = 0.005 cm
CALCULATION: h = a-b=0.124-0.005=0.119 (ii) Mean Value between two legs of spherometer =2.9 cm (i)
(iii) R = (iv)
2
l 6h
h 2
+ =0.119/2+8.41/6*0.119 =11.838
= 1 + R f
=
RESULTS: 1. The refractive index of other liquid
=
PRECAUTIONS: 1. The plane mirror should be clean and fully shining surface. 2. The liquid taken should be transparent. 3. The parallax should be removed tip to tip. 4. The eye should be at a distance about 30 cm from the needle while removing the parallax. 5. Only few drops of liquid should be taken so that its layer should be thick. 6. The legs of the spherometer should be vertical. 7. The centre leg of the spherometer should turn in one direction only.
SOURCES OF ERROR: 1. Liquid may not be quite transparent. 2. The parallax may not be fully removed. 3. The spherometer legs should be placed symmetrical on the surface of the convex lens. 4. The tip of the central screw should not just touch the surface of lens or mirror.
INDEX Objective And Apparatus Diagram Theory Procedure Observations Calculations Results Precautions Sources Of Errors
PLANE MIRROR: A plane mirror is a mirror with a flat ( planar ) reflective surface. For light rays striking a plane mirror, the angle of reflection equals the angle of incidence.
The angle of incidence is the angle between the incident ray and the normal .The image formed by a plane mirror is always virtual ,upright, and of the same shape and size as the object it is reflecting. Plane mirrors are the only type of mirror for which a real object always produces an image that is virtual, erect and of the same size as the object. The focal length of a plane mirror is infinity; its optical power is zero.
CONVEX LENS: An optical lens is generally made up of two spherical surfaces. If those surfaces are bent outwards or convex, the lens is called a biconvex lens or simply convex lens. These lenses can converge a beam of light coming from outside and focus it to a point on the other side. This point is known as the focus and the distance between the centre of the lens to the focus is called the focal length of convex lens The lens in the human eyes is a biconvex lens. So the most common use of the lens is that it helps us to see. It is used to correct Hypermetropia or long-sightedness. It is used in cameras because it focuses light and produces a clear and crisp image. It is also used in other magnifying devices such as microscopes and telescopes.
SPHEROMETER : A spherometer is an instrument for the precise measurement of the radius of curvature of a sphere or a curved surface. Originally, these instruments were primarily used by opticians to measure the curvature of the surface of a lens The Spherometer consists of a micrometer screw threaded into a small tripod with a vertical scale fastened to it. The head of the screw has a graduated disk used to measure fractional turns of the screw. The vertical scale is used to measure the height or depth of the curvature of the surface. The vertical scale divisions are on 1 mm, which is the pitch of the threads of the screw. The head of the screw is graduated into 100 divisions.
