Radiant Flux Through Apertures— III

This paper completes our treatment of radiant flux through pairs of apertures. In Part II, we obtained approximate equations for rectangular apertures in parallel planes, with the restriction that two apertures be identical and that one be directly above the other. Here we generalize to the case of any apertures that fit into a rectangular grid. The idea for this generalization originated with Ondracek but it is here expressed in matrix notation, which allows coefficients F_ij to be obtained rather simply.     

Radiant flux through apertures—I

Equations for the calculation of radiant power F through two apertures in series are well known. A characteristic of these formulae is that they give F as a small difference between two large terms. Evidently, the flux through the apertures must decrease as the spacing between them increases; and for large spacing, the inverse-square relation must hold. Instead of exhibiting this behaviour in an obvious manner, however, the traditional equations give the specious impression of an increase in F with increase in spacing. The paper develops an approximate formulae that applies to apertures in the shape of any regular polygon and that shows clearly how the inverse square relation is approached for large separation.     

Simplified interflection calculations

The purpose of the paper has been to present simplified methods that will expedite the calculation of ceiling lighting (Type II). Approximate formulas have been given, which allow ordinary slide-rule calculations to be made very easily for the usual range of variables. Only with rooms having very high domance (or perhaps with extraordinarily high floor reflectance) are the complicated equations of the previous paper (1) needed. These approximate formulas can be represented also by alignment charts, Figs. 2 to 5, which further simplify the work.Either the formulas or the charts may be used to investigate the effect of a change in ?₁, ?₂, or ?₃. However, if reflectances are standardized at recommended values, other methods are possible.In particular, one may use graphs (Fig. 6) or a slide-rule (Figs. 7 and 8). The method of calculation chosen for a specific problem will depend on the problem and on the preferences of the designer. The previous equations and tables (3) may always be used; but in most cases, time can be saved by employing the short-cuts given in the present paper.     

Separability in a class of coordinate systems

A study is made of separability conditions for the Helmholtz and Laplace equations. Attention is confined to the most useful case for physical applications; namely,

1.

(a) The coordinate system is either cylindrical or it has rotational symmetry, and     

Interflectance calculations for various luminaires

Previous interflectance tables have dealt principally with three basic types of lighting (Types I, II, and III). The present paper extends the scope of the interflection method by showing how it can be applied to rooms lighted by hanging luminaires. It is found that most cases arising in practice can be covered by six canonic distributions. The effect of mounting height is handled by means of a simple equation.     

Utility value interventions in a college biology lab: The impact on motivation

Science writing, such as lab reports, allows students to form a meaningful understanding of scientific concepts. However, students often view scientific writing as unimportant and utilize surface level approaches when completing writing assignments. The current study implemented three experimental interventions (directly-communicated, self-generated, and hybrid) aligned with prior literature and designed to improve the utility value of lab reports in college settings. Participants (n = 1,002) were recruited from 43 lab sections of an introductory biology course at a large southeastern university. Measures of subjective task value (utility value, attainment value, cost, and intrinsic value) were collected pre-, mid-, and post-intervention. The self-generated and hybrid groups exhibited higher self-reported utility value by posttest compared to the control group. Requiring students to generate their own utility value toward a task, followed by a written reflection, increases students' maintained and situational interest for biology laboratory reports.