Equi-convex lens, plane mirror, a thin needle, iron stand with clamp, water and oil, spherometer, metre scale
By lens-makers formula 𝑛𝑔 1 1 1 ( − 1) ( − ) = 𝑛𝑙 𝑅1 𝑅2 𝑓 Where: ng: Refractive index of lens glass nl : Refractive index of liquid used R1: Radius of curvature of side 1 of lens R2: Radius of curvature of side 2 of lens From the experiment we can find f (focal length) R1 and R2 (Radius of curvatures) can be measured ng is known or easily calculated when experiment is done in air Hence nl can be calculated by using the lensmakers formula
Finding Radius of Curvature of lens: 1) 2) 3)
4) 5)
6)
7)
Determine the least count and pitch of the spherometer. Rotate the screw till it is at zero. Put the lens on the flat surface and place the spherometer on top, and rotate the screw till all 3 legs and tip of screw meet lens surface. Note down circular scale reading (call it a1). Place the spherometer on a flat surface and rotate the screw till 3 legs and tip of screw meets the surface. Note down the reading in circular scale (call it a2) and number of complete rotations (call them n). Press the 3 legs of spherometer on a sheet of paper. Using the marks draw a triangle and measure the length of each side (l1,l2 and l3).
8) 9)
Repeat the steps 2-6 three times and note it down. After determining the height divide it by 2 and use it to find radius of curvature (Call it R) (This due the reason that lens is equiconvex in nature).
Finding focal length of lens: 1) 2) 3) 4)
5)
6) 7)
Place the plane mirror on the floor or on the base of iron stand. Fix the clamp and clamp the needle. Place the lens on the plane mirror. Adjust the needle and lens such that the tips object needle and image needle appear at the centre of lens. Adjust the clamp height so that both object needle and image needle are of same size, tips coincide and move simultaneously at same speed. Note down the height of needle from plane mirror (call it x1). Note down the height of needle from the
8) 9)
surface of lens (call it x2). Repeat steps 5-7 three times. Take the average of the value of x1 and x2. This is your focal length (f).
Finding refractive index of material the lens is made of: 1) 2) 3) 4) 5)
Take R2 as infinity. (Due to plane mirror) Take R1 as R. Use f as fa. Here nl=1 as medium is air. Using lens maker formula calculate the value of refractive index of lens ng.
Finding focal length of lens with liquid: 1)
Place the plane mirror on the floor or on the base of iron stand. 2) Fix the clamp and clamp the needle. 3) Pour the liquid on the mirror. (Use water first so as water is easier to clean) 4) Place the lens on the plane mirror on the liquid layer. 5) Adjust the needle and lens such that the tips object needle and image needle appear at the centre of lens. 6) Adjust the clamp height so that both object needle and image needle are of same size, tips coincide and move simultaneously at same speed. 7) Note down the height of needle from plane mirror (call it x1). 8) Note down the height of needle from the surface of lens (call it x2). 9) Repeat steps 5-7 three times. 10) Take the average of the value of x1 and x2. This is your focal length (fw).
11) Repeat this experiment with oil as liquid and take the focal length to be fo.
Finding refractive index of material the liquid: 1) 2) 3) 4) 5)
Take R2 as infinity. (Due to plane mirror) Take R1 as R. Use f as fw. Using the value of ng find nl which here is nw. Repeat this experiment with f as fo and nl to be no.
For Radius of Curvature of lens: Least count of spherometer: 0.001 cm Sl.No Circlular scale reading Lens a1×L.C (cm)
Flat area a2×L.C (cm)
If n=0 No h=(100+a1)-a2 of turns If n≠0
1) 2) 3)
h=(n×100+a1)-a2
(cm)
h1= h2= h3=
Distance between legs of spherometer 𝑙1 + 𝑙2 + 𝑙3 𝑙= 3 l= cm
Height ℎ =
(
ℎ1 +ℎ2 +ℎ3 )⁄ 3
h=
2
cm
Radius of curvature 𝑅 =
𝑙2 6ℎ
+
R=
ℎ2 2
cm
For focal length of lens: Sl.No Distance of needle from Mirror x1 (cm) Lens x2 (cm) 1) 2) 3) Focal length 𝑓 = f=
𝑓1 +𝑓2 +𝑓3 3
cm
𝑓=
𝑥1 + 𝑥2 2
(cm) f1= f2= f3=
For focal length of lens with water: Sl.No Distance of needle from Mirror x1 (cm) Lens x2 (cm) 1) 2) 3) Focal length 𝑓𝑤 =
𝑓𝑤 =
𝑥1 + 𝑥2 2
(cm) f1= f2= f3=
𝑓1 +𝑓2 +𝑓3 3
fw=
cm
For focal length of lens with oil: Sl.No Distance of needle from Mirror x1 (cm) Lens x2 (cm) 1) 2) 3) Focal length 𝑓𝑜 = fo=
𝑓1 +𝑓2 +𝑓3 3
cm
𝑓𝑜 =
𝑥1 + 𝑥2 2
(cm) f1= f2= f3=
Calculating refractive index: Without any liquid 𝑹 𝒏= +𝟏 𝒇 Hence refractive index of lens n= With water: 𝑹 𝒏 = 𝒏𝒈 ( + 𝟏) 𝒇𝒘 Hence refractive index of water nw= With oil: 𝑹 𝒏 = 𝒏𝒈 ( + 𝟏) 𝒇𝒐 Hence refractive index of oil no=
Refractive index of water is: Refractive index of oil is:
1) 2) 3) 4)
Plane mirror should be completely clean. Liquid taken should be transparent. Parallax error should be removed. Only add few drops of liquid is to be poured on mirror. 5) Legs of spherometer should be vertical. 6) To prevent backslash error in spherometer rotate the screw in one direction. 1) Liquid may not be transparent. 2) Parallax may not be fully removed. 3) Legs of spherometer should be placed evenly on convex lens. 4) Tip of screw of spherometer should just touch the surface.
This project in overall finds the refractive index of any transparent liquid and also verifies lens maker’s formula.
