Aim
To determine the refractive index of glass by comparing the real depth and the apparent depth of a mark seen through glass blocks.
Variables
- Manipulated: Real depth of the mark, H (using glass blocks of different thickness)
- Responding: Apparent depth of the mark, h
- Constant: The same type of glass and the same viewing method
Apparatus & materials
- Glass blocks of several thicknesses
- Travelling microscope
- A mark or pin on paper
- Lycopodium powder
- Ruler
Procedure
- Make a clear mark on paper and place it on the microscope stage; focus the microscope on the mark and record the reading (bottom).
- Place a glass block on the mark; focus on the image of the mark seen through the glass and record the reading (image).
- Sprinkle a little lycopodium powder on the top of the block; focus on the powder and record the reading (top).
- Find the real depth H = top − bottom and the apparent depth h = top − image.
- Repeat with glass blocks of different thickness.
- Record H and h for each block.
Tabulating results
Record the real depth H and the apparent depth h in cm (or mm) for each block. You may add a column for the ratio H / h.
The graph
Plot the real depth H (y-axis) against the apparent depth h (x-axis). A straight line through the origin shows H is directly proportional to h; the gradient is the refractive index.
Analysis
The refractive index is n = real depth / apparent depth = H / h. The gradient of the H against h graph gives the refractive index of the glass.
Precautions
- Focus the microscope carefully and avoid parallax when taking each reading.
- Keep the microscope vertical so all readings are measured along the same line.
- Use a fine mark and a thin layer of powder for sharp focusing.
Light and Optics · Graph skills
Sample results and what they show
These are example readings for the real depth H and apparent depth h of a mark viewed through glass blocks of increasing thickness, each measured with a travelling microscope.
- H = 3.0 cm, h = 2.0 cm, H/h = 1.50
- H = 4.5 cm, h = 3.0 cm, H/h = 1.50
- H = 6.0 cm, h = 4.0 cm, H/h = 1.50
- H = 7.5 cm, h = 5.0 cm, H/h = 1.50
- H = 9.0 cm, h = 6.0 cm, H/h = 1.50
The apparent depth is always less than the real depth, so a mark under glass looks closer to the top than it truly is. This happens because light from the mark bends away from the normal as it leaves the glass, so the mark appears raised.
Working out H ÷ h for each thicker block gives the same value, close to 1.50, throughout. That fixed ratio is the message of the experiment: it is the refractive index of the glass, and it does not depend on how thick the block is.
Reading the graph and finding the answer
Plot the real depth H on the y-axis against the apparent depth h on the x-axis. The points lie on a straight line passing through the origin, showing H is directly proportional to h.
Take a large triangle on the best-fit line using two well-separated points, for example (2.0 cm, 3.0 cm) and (6.0 cm, 9.0 cm):
- gradient = (9.0 − 3.0) cm ÷ (6.0 − 2.0) cm = 6.0 cm ÷ 4.0 cm = 1.50
The gradient has no unit because it is a ratio of two lengths, and it equals the refractive index n of the glass. So n = 1.50.
Read the two coordinates from the drawn line, not from raw points, since the line has been fitted to all the data. The SPM Physics 4531 papers give no formula sheet, so recall n = real depth / apparent depth yourself.
Choose axis scales that spread the plotted points across more than half of the grid, and draw the best-fit line so the points are balanced evenly on both sides of it. If one point is clearly off the line, treat it as an anomalous reading, ring it, and leave it out when drawing the line and taking the gradient.
Marks examiners look for
Precautions that keep the depths accurate:
- Focus the travelling microscope carefully and take each reading at the same setting to avoid parallax.
- Keep the microscope vertical so all three readings lie on one line.
- Use a fine mark and only a thin dusting of lycopodium powder for a sharp focus.
- Avoid touching the bench while reading so the microscope does not shift.
For the Paper-3 science process skills, examiners award marks for: naming the manipulated variable (real depth H, by changing block thickness), responding variable (apparent depth h) and constant (the same type of glass); tabulating H and h with consistent units and decimals; plotting at least five points with labelled axes and a best-fit line through the origin; and finding the gradient with a large triangle. State that H is proportional to h and quote the refractive index as the conclusion.
Repeat each reading and take the average to reduce random error, and quote the final answer to a sensible number of significant figures with its correct unit. In the discussion, name one source of error together with a matching improvement, and note that any point off the line was ignored so the conclusion rests on consistent data.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)