Physics Chapter: Diffraction and Lenses

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Questions and Answers

What is the approximate value of di1 calculated in part a using the given equation?

40.5mm

70.0mm

53.8mm (correct)

65.2mm

What value did we derive for the magnification (M1) in part a?

-1.0

0.54

1.54

-0.54 (correct)

What is the formula used to derive di1 from the given parameters?

di1 = f1 d01 / (d01 + f1)

di1 = f2 d02 / (d02 + f1)

di1 = d01 f1 / (d01 + f2)

di1 = f1 d01 / (d01 - f1) (correct)

In the context of the lens system, how is di2 determined according to the thin lens equation?

di2 = f2 d02 / (d02 - f2) Signup and view all the answers

What does the negative sign in the magnification (M1) indicate about the image?

The image is inverted. Signup and view all the answers

What happens to the object distance (do) as the magnification (|M|) increases significantly?

do approaches the focal point (f). Signup and view all the answers

If the magnification (M) is equal to 100, what are the possible distances for the object distance (do)?

do = 99 or do = 101. Signup and view all the answers

According to the relationship established in the content, how does a change in M affect the image distance (di)?

di changes and must be adjusted when M changes. Signup and view all the answers

What equation can be derived from rearranging the relation given between di and do in the content?

do = f(M - 1) / M. Signup and view all the answers

Why might achieving high magnifications be practically impossible in real-life applications?

Higher magnifications demand the object to be very close to the focal point, making alignment difficult. Signup and view all the answers

What is the formula for calculating the slit width in single slit diffraction?

$D = \frac{m\lambda L}{x}$ Signup and view all the answers

What happens to the spacing between minima as the slit width decreases?

It becomes wider. Signup and view all the answers

If the wavelength $\lambda$ increases, what effect does it have on the spacing between minima?

It increases the spacing. Signup and view all the answers

What is the estimated value of the slit width D from the calculations?

265.1 μm Signup and view all the answers

At what position on the screen does the first minima occur according to the formula?

$1.75 \times 10^{-2} m$ Signup and view all the answers

What does the variable L represent in the context of the single slit diffraction equation?

The distance from the slit to the screen. Signup and view all the answers

Given the maximum and minimum values calculated, what is the uncertainty in the slit width measurement?

±0.75 μm Signup and view all the answers

What is the effect on the minima pattern if the distance L is decreased?

The minima pattern will converge. Signup and view all the answers

What is the value of di2 as calculated from the given expressions?

384mm Signup and view all the answers

What is the formula used to calculate magnification M2?

M2 = - (di2/(do2 * (L - di1))) Signup and view all the answers

How is the overall magnification Mtot calculated from the individual magnifications?

Mtot = M1 × M2 Signup and view all the answers

If L is 300mm and di1 is calculated to be 150mm, what expression is used to find the value of di2?

(L - di1) - f2 Signup and view all the answers

What is the significance of the negative sign in the magnification formula M2?

It signifies inversion of the image. Signup and view all the answers

Which of the following represents a plausible value for L given the context?

300mm Signup and view all the answers

When multiplying the two magnifications M1 and M2, which variable is NOT necessary?

L Signup and view all the answers

From the equations provided, what can be inferred about the relationship between di2 and f2?

di2 depends inversely on f2. Signup and view all the answers

What is the total magnification (Mtot) based on the provided formula?

0.84 Signup and view all the answers

What does a positive magnification indicate about the image?

The image is upright. Signup and view all the answers

What happens to di2 when di1 approaches infinity?

di2 approaches f2. Signup and view all the answers

What is the final value of Mtot when do1 equals f1 and di1 approaches infinity?

-4.29 Signup and view all the answers

What is inferred if the magnification (Mtot) is negative?

The image is inverted. Signup and view all the answers

In the provided expression for Mtot, which variables directly influence the final magnification when adjusted?

focal lengths of the lenses. Signup and view all the answers

Why is it practical to analyze the final magnification over long distances?

Because the final magnification remains consistent irrespective of lens positioning. Signup and view all the answers

What is the role of L in the magnification formulas discussed?

It is irrelevant to the final magnification. Signup and view all the answers

Study Notes

Single Slit Diffraction

The position of the minima for a single-slit diffraction pattern can be calculated using the following formula:
- x = (mλL) / D
- m is the order of the minima,
- λ is the wavelength of light,
- L is the distance from the slit to the screen,
- D is the width of the slit.
If the slit width decreases, the spacing between minima will increase.
If the distance L increases, the spacing between minima will also increase.

Thin Lens Equation

The thin lens equation relates the distance do of the object from the lens, the distance di of the image from the lens and the focal length f of the lens:
- 1/f = 1/do + 1/di
Magnification is the ratio of the image size to the object size:
- M = (di) / (do)
For a thin lens, the magnification is inversely proportional to the distance do from the lens.
To achieve high magnification, the object distance do needs to be very close to the focal length f, which can cause alignment issues in practice.
If M changes, so will do.
To keep the image at the detector, the detector must be adjusted whenever the magnification M changes.

Two Lens System

The distance of the image formed by the first lens to the second lens is given by do2 = L − di1
The overall magnification for a two-lens system is the product of the magnifications of the individual lenses:
- Mtot = M1 × M2
The final magnification for a two-lens system with the object at do1 = f1 and the image at di1 → ∞ is:
- Mtot = −f2 / f1
- This magnification is independent of the distance L between the lenses.

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Description

This quiz covers key concepts related to single-slit diffraction and the thin lens equation. You'll explore how changes in slit width and object distance affect diffraction patterns and magnification. Test your understanding of these important principles in optics.