# (a) Interpretation: A spread sheet should be created to determine the Bragg wavelength for the given information. Concept introduction: Couple wave theory will be used to determine the behavior of holographic filters. For a holographic optical element, the Bragg wavelength λ b is determined by: λ b =2ndcosθ Where the grating material’s refractive index is n, grating period is d and the angle of incidence of the radiation beam is given by θ . ### Principles of Instrumental Analysis

7th Edition
Douglas A. Skoog + 2 others
Publisher: Cengage Learning
ISBN: 9781305577213 ### Principles of Instrumental Analysis

7th Edition
Douglas A. Skoog + 2 others
Publisher: Cengage Learning
ISBN: 9781305577213

#### Solutions

Chapter 7, Problem 7.24QAP
Interpretation Introduction

## (a)Interpretation:A spread sheet should be created to determine the Bragg wavelength for the given information.Concept introduction:Couple wave theory will be used to determine the behavior of holographic filters. For a holographic optical element, the Bragg wavelength λb is determined by:λb=2ndcosθWhere the grating material’s refractive index is n, grating period is d and the angle of incidence of the radiation beam is given by θ.

Interpretation Introduction

### (b)Interpretation:The angle at which the Bragg wavelength is 462 nm should to calculated.Concept introduction:Couple wave theory will be used to determine the behavior of holographic filters. For a holographic optical element, the Bragg wavelength λb is determined by:λb=2ndcosθWhere the grating material’s refractive index is n, grating period is d and the angle of incidence of the radiation beam is given by θ.

Interpretation Introduction

### (c)Interpretation:The reason why the Bragg wavelength is also said to be “playback wavelength” at times should be determined.Concept introduction:Couple wave theory will be used to determine the behavior of holographic filters. For a holographic optical element, the Bragg wavelength λb is determined by:λb=2ndcosθWhere the grating material’s refractive index is n, grating period is d and the angle of incidence of the radiation beam is given by θ.

Interpretation Introduction

### (d)Interpretation:The historical significance of the Bragg wavelength should be determined.Concept introduction:Couple wave theory will be used to determine the behavior of holographic filters. For a holographic optical element, the Bragg wavelength λb is determined by:λb=2ndcosθWhere the grating material’s refractive index is n, grating period is d and the angle of incidence of the radiation beam is given by θ.

Interpretation Introduction

### (e)Interpretation:The angular tuning range of the given filer should be determined.Concept introduction:Couple wave theory will be used to determine the behavior of holographic filters. For a holographic optical element, the Bragg wavelength λb is determined by:λb=2ndcosθWhere the grating material’s refractive index is n, grating period is d and the angle of incidence of the radiation beam is given by θ.

Interpretation Introduction

### (f)Interpretation:The Bragg wavelength and the wavelength range of the given filter should be determined.Concept introduction:Couple wave theory will be used to determine the behavior of holographic filters. For a holographic optical element, the Bragg wavelength λb is determined by:λb=2ndcosθWhere the grating material’s refractive index is n, grating period is d and the angle of incidence of the radiation beam is given by θ.

Interpretation Introduction

### (g)Interpretation:The applications of tunable holographic filters should be determined.Concept introduction:A hologram is an image which appears as three dimensional and it can be seen through bare eye. The technology of making and using of holograms is said to be holography.

Interpretation Introduction

### (h)Interpretation:The refractive index modulation in a given film should be determined.Concept introduction:Couple wave theory will be used to determine the behavior of holographic filters. For a holographic optical element, the Bragg wavelength λb is determined by:λb=2ndcosθWhere the grating material’s refractive index is n, grating period is d and the angle of incidence of the radiation beam is given by θ.

Interpretation Introduction

### (i)Interpretation:The expression for ideal grating efficiency and its value should be determined.Concept introduction:Couple wave theory will be used to determine the behavior of holographic filters. For a holographic optical element, the Bragg wavelength λb is determined by:λb=2ndcosθWhere the grating material’s refractive index is n, grating period is d and the angle of incidence of the radiation beam is given by θ.

Interpretation Introduction

### (j)Interpretation:The efficiency for a given grating should be determined.Concept introduction:For the real grating, the refractive index modulation is described by:△n=λsin−1DeπtWhere De is the grating efficiency.

Interpretation Introduction

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