Discovering the Distance at Which Two Light Bulbs Appear as One
How can we determine the distance at which two light bulbs will appear as a single light bulb?
We have two light bulbs separated by 1 meter. Will they appear as one bright light bulb in this scenario?
Answer:
When two light bulbs are separated by a certain distance, their appearance as a single light bulb depends on the angular separation between them compared to the minimum angle of resolution. Let's delve into the calculation to find out more.
Exploring the Concept of Angular Separation and Minimum Angle of Resolution
When analyzing the scenario of two light bulbs being 1 meter apart, the first step is to determine the minimum angle of resolution. This parameter is crucial as it signifies the smallest angle at which the human eye can distinguish two separate points.
The formula to calculate the minimum angle of resolution is: Minimum Angle of Resolution (θ) = 1.22 * (wavelength / pupil diameter).
Substitute the values of the green light's wavelength (0.5 micron) and the human eye's pupil diameter (3 mm) into the formula to find θ.
Once we have the minimum angle of resolution (θ), we can calculate the angular separation between the two light bulbs. This separation is determined by the formula: Angular Separation (α) = Object Distance / Distance between light bulbs. Plugging in the given values, we can calculate α.
By comparing the angular separation (α) to the minimum angle of resolution (θ), we can conclude whether the two light bulbs will appear as a single light bulb. If α is less than or equal to θ, they will merge into one bright light bulb.
In the scenario of two light bulbs separated by 1 meter, the angular separation of 1 radian surpasses the minimum angle of resolution of 2.03 x 10^-4 radians. Therefore, the two light bulbs will not appear as a single light bulb in this setup.
To summarize, when the two light bulbs are spaced 1 meter apart, their angular separation exceeds the minimum angle of resolution, resulting in them being perceived as individual light sources rather than a unified one.