Refractive index of a liquid using a convex lens and a plane mirror (Class 12 practical)

Aim

To find the refractive index of a liquid using convex lens and plane mirror.

Apparatus and material required

• •Thin equiconvex (double convex) lens, focal length about 20 cm
• •Plane mirror, larger than the lens
• •Laboratory stand with a clamp holding a pin horizontally
• •Metre scale and plumb line
• •Water (or the given liquid) and a dropper
• •Spherometer (to measure the radius of curvature R of the lens)

Principle

Refractive index of a liquid: convex lens and plane mirror: formulas and key facts

Lenses in contact

$\frac{1}{F}=\frac{1}{f}+\frac{1}{f_w}$

Focal length of the liquid lens

$f_w=\frac{fF}{f-F}$

Comes out negative: the liquid lens is plano-concave (diverging).

Lens maker's formula for the plano-concave liquid lens

$\frac{1}{f_w}=(n-1)\left(\frac{1}{\infty }-\frac{1}{R}\right)$

Refractive index of the liquid

$n=1+\frac{R}{|f_w|}$

Distance of pin from the optical centre

$f=\frac{d_1+d_2}{2}$

d₁: pin to top surface of the lens; d₂: pin to the plane mirror.

Key facts

• •Pin at focus: image coincides with the pin
• •Liquid forms a plano-concave lens
• •Combination focal length F is greater than f
• •Pin moves up after filling water
• •Water: n about 1.33 (NCERT data table)
• •Use a thin lens and a horizontal mirror

Procedure

1. 1Measure the radius of curvature R of the lens surface with a spherometer (Class XI method).
2. 2Place the plane mirror on the base of the stand, reflecting surface up, and put the convex lens on it.
3. 3Clamp a bright pin horizontally above the lens, with its tip vertically above the optical centre (use a plumb line).
4. 4Move the pin up or down until the tip of its inverted image just touches the tip of the pin with no parallax.
5. 5Measure the distance of the pin from the top surface of the lens (d₁) and from the mirror (d₂); f = (d₁ + d₂)/2.
6. 6Lift the lens, put a few drops of water on the mirror with a dropper and place the lens back, so water fills the space without air bubbles.
7. 7Raise the pin and again remove parallax between the pin and its image. Measure d₃ and d₄; F = (d₃ + d₄)/2.
8. 8Repeat each measurement three times and find f_w and n for each set.

Observation table

Draw the table like this in your record. The numbers are sample readings to show how it is filled in; use your own.

Calculation

1. 1.Row 2: $f_w=\frac{fF}{f-F}=\frac{20.1\times 30.3}{20.1-30.3}=\frac{609.0}{-10.2}=-59.7$ cm
2. 2.Row 2: $n=1+\frac{R}{|f_w|}=1+\frac{20.0}{59.7}=1.335$
3. 3.Mean of the three rows: n = (1.331 + 1.335 + 1.341)/3 = 1.336
4. 4.Check: NCERT's data section gives 1.333 for water, so the sample result is within 0.003 of it.

Result

The refractive index of the given liquid (water) is n = ____ (sample: 1.336).

Precautions

• →Keep the pin horizontal, with its tip on the vertical axis through the optical centre of the lens.
• →Use a thin lens, and measure the pin's distance from both the lens surface and the mirror, taking the mean.
• →Put the water in gently with a dropper, without moving the lens and without trapping air bubbles.
• →Keep the plane mirror horizontal.
• →Remove parallax tip to tip; the image tip should touch the pin tip, not overlap it.

Sources of error

• •The two surfaces of the lens may not have exactly the same radius of curvature.
• •The plane mirror may not be horizontal.
• •The lens may not be thin, so the mean distance is not exactly from the optical centre.
• •Error in measuring R with the spherometer.

Viva questions with answers

Say your answer out loud first, then open the card. Examiners want one or two clear sentences, not a paragraph.

1. 1.Why does the image coincide with the pin when the pin is at the focus?Show answer

   Rays from the focus leave the lens parallel to the axis, fall normally on the plane mirror, retrace their path, and come back to the same point, forming an image at the pin itself.

2. 2.What type of lens does the water form?Show answer

   A plano-concave lens: its upper surface takes the curvature of the convex lens and its lower surface is flat on the mirror.

3. 3.Why must the pin be raised after filling water?Show answer

   The water lens is diverging, so the combination has a longer focal length than the glass lens alone (F > f).

4. 4.Write the formula for two thin lenses in contact.Show answer

   $1/F=1/f_1+1/f_2$.

5. 5.State the lens maker's formula.Show answer

   $1/f=(n-1)(1/R_1-1/R_2)$, for a thin lens in air.

6. 6.Why is the focal length of the water lens negative?Show answer

   A plano-concave lens is diverging. Also, F > f in fF/(f − F) makes the denominator negative.

7. 7.What is the refractive index of water?Show answer

   About 1.33; NCERT's data table gives 1.333.

8. 8.Why is a thin lens used?Show answer

   So that distances measured from its surface are almost the same as from the optical centre.

9. 9.What is the use of the plumb line?Show answer

   To check that the pin tip lies on the vertical through the optical centre, so the rays retrace their path.

10. 10.What would happen if the liquid had the same refractive index as the glass?Show answer

    The lower glass surface would no longer bend light, so lens and liquid together act as a plano-convex lens of radius R. Its focal length is R/(n − 1), twice that of the equiconvex lens, so F = 2f.

11. 11.How do you measure R?Show answer

    With a spherometer, as in the Class XI experiment, on the lens surface that touches the liquid.

12. 12.Would a liquid of higher refractive index need the pin higher or lower than with water?Show answer

    Higher. A larger n makes the liquid lens more strongly diverging, so F is larger.

Viva practice: these questions one at a time, with the answer hidden until you ask, and a tally of what to revise.

Common mistakes in the practical exam

The slips examiners see most often, and what to write instead.

• ✗Mistake: Measuring the pin's distance only from the top of the lens.

  ✓Do this: Measure from the lens surface and from the mirror, and take the mean as f (or F).

• ✗Mistake: Dropping the minus sign of f_w and then writing n = 1 − R/f_w.

  A sign slip gives n less than 1, which is impossible.

  ✓Do this: Use n = 1 + R/|f_w|, and check that n comes out between 1.3 and 1.5 for common liquids.

• ✗Mistake: Using f instead of R in n = 1 + R/|f_w|.

  ✓Do this: R is the radius of curvature from the spherometer, not the focal length of the lens.

• ✗Mistake: Trapping air bubbles in the water layer.

  ✓Do this: Put a few drops on the mirror first and lower the lens gently onto them.

• ✗Mistake: Drawing the ray diagram without the rays retracing their path.

  ✓Do this: Show rays from the pin through the lens, normal to the mirror, and back along the same path.

Refractive index of a liquid: convex lens and plane mirror: frequently asked questions