In the following experiment, we want to measure the slit width of our telescope using the spectral lines of an Hg-lamp. We place a grating and a prism between the lamp and the slit and determine the angular difference of the Hg lines. From the values obtained, we also determine the resolving power.
Table of Contents
1 Introduction
2 Basics
2.1 Preparation questions
2.2 Theoretical Basics
2.2.1 Derivation of the resolution power - Grid
2.2.2 Derivation of the resolution power - Prism
2.2.3 Diffraction vs. prism spectrum
3 Experimental setup and Realization
3.1 Experimental setup
3.2 Realization
4 Measurement results and evaluation
4.1 Measurement of the zero point
4.2 Measurement of the slit size - Prism
4.3 Measurement of the slit size - Grid
5 Conclusion
6 Data
6.1 Measuring the zero point
6.2 Measurement 2 - Prism
6.3 Measurement 3 - Grid
Research Objectives and Topics
The primary goal of this experiment is to determine the slit width of a telescope by analyzing spectral lines from a mercury (Hg) lamp. The study investigates how different optical components, specifically a diffraction grating and a prism, allow for the calculation of angular differences in spectral lines and the subsequent derivation of the optical resolving power.
- Measurement of telescope slit width using an Hg-lamp.
- Application of prism-based spectral analysis.
- Application of diffraction grating-based spectral analysis.
- Derivation and comparison of resolving power equations.
- Evaluation of experimental accuracy versus theoretical values.
Excerpt from the Book
2.2.1 Derivation of the resolution power - Grid
Two points of light can only be perceived separately by the observer if the main maximum of the second point of light falls within the first minimum of the first point of light.
As we know the intensity is defined as:
I(α) = I0 sin^2(Nπg/λ sin α) / sin^2(πg/λ sin α)
Because of the condition mentioned above we know that:
Nπg/λ sin αmax = π + Nπg/λ sin αmin
⇔ Nπg/λ Δ sin α = π
Where Δ sin α = sin αmax − sin αmin. We can now calculate the first order Taylor series of Δ sin α:
Δ sin α ≈ cos α · Δα
In conclusion we get:
Δα = λ / (Ng cos α)
If we now calculate the derivative (grid equation):
dλ / dα = k / (g cos(α))
Where k is the diffraction order. If we assume dλ/dα = λ/Δα the result is the following:
λ / Δλ = (Ngk cos α) / (g cos α) = kN (1)
Summary of Chapters
1 Introduction: This chapter outlines the experiment's objective to measure slit width and resolving power using an Hg-lamp, prism, and grating.
2 Basics: This section provides the theoretical foundation, including preparation questions and the mathematical derivations for resolution power regarding grids and prisms.
3 Experimental setup and Realization: Describes the necessary equipment and the step-by-step procedural approach for the measurements performed.
4 Measurement results and evaluation: Presents the calculated values for the zero point, slit width, and resolving power based on the collected experimental data.
5 Conclusion: Summarizes the findings, confirming that the experimental results align closely with theoretical expectations.
6 Data: Provides the raw measurement tables collected during the different stages of the experiment.
Keywords
Spectroscopy, Hg-lamp, Slit width, Resolving power, Diffraction grating, Prism, Angular difference, Optical resolution, Experimental physics, Spectral lines, Wave-length, Measurement deviation.
Frequently Asked Questions
What is the core focus of this experimental protocol?
The protocol documents the process of measuring the slit width of a telescope and determining its resolving power by utilizing spectral lines produced by an Hg-lamp.
What are the central thematic areas?
The central themes include optics, spectral analysis, diffraction grating theory, and prism-based light refraction.
What is the primary objective of this work?
The objective is to empirically determine optical parameters—specifically slit width and resolution—and validate these results against theoretical physical models.
Which scientific methods are utilized?
The experiment employs comparative analysis between prism and grating spectra, utilizing linear approximation and mathematical derivations based on the Fermat principle and the grid equation.
What topics are covered in the main section?
The main sections cover the theoretical derivation of resolution, the experimental setup, procedures for calculating slit size, and the analysis of measured data.
How are the key results characterized?
The results are characterized by a high level of accuracy, with calculated values showing only slight deviations from the theoretical predictions.
How does the resolution power differ between the prism and the grid?
The protocol derives separate mathematical models for both: the prism resolution depends on the refractive index gradient, while the grid resolution is derived from diffraction orders.
Why was it necessary to approximate the slit width in the grid experiment?
The authors noted that they did not record the physical slit width at the conclusion of that specific experimental segment, necessitating an indirect calculation based on collected data.
- Quote paper
- Tim Peinkofer (Author), 2025, Protocol AG. Resolution. Resolving Power and Slit Width via Hg Lamp Spectra, Munich, GRIN Verlag, https://www.grin.com/document/1688256
