In three arrangements, you view two closely spaced small objects that are the same large distance from you. The angles that the objects occupy in your field of view and their distances from you are the following: (1) $2\varphi$and ; (2) $2\varphi$and $2R$; (3) $\varphi /2$and $R/2$. (a) Rank the arrangements according to the separation between the objects, with the greatest separation first. If you can just barely resolve the two objects in arrangement 2, can you resolve them in (b) arrangement 1 and (c) arrangement 3?

The radius in experiment 1 is R and angle is$\varphi$ .

The radius in experiment 2 is 2R and angle is$2\varphi$ .

The radius in experiment 3 is $R/2$and angle is$\varphi /2$ .

The expression to calculate the distance between the objects is given as follows.$\mathrm{d}=\mathrm{\theta l}$

Here, d is the distance between the objects, I is distance between the observer and

and $\mathrm{\theta }$is the angle.

The distance between the two objects depends on the angles occupied by both objects. Therefore, the distance between the two objects is greater, which occupies a large angle.

Consider the figure below, which shows the arrangement of the experiments.

From the above, the angle occupied by the object in experiments 1 and 2 is the same. Therefore, the angle distance between the two objects for experiments 1 and 2 is the same. Since the angle of the experiment is less as compared to the other two experiments, the distance between the objects is also less compared to experiments 2 and 3.

Hence, the rank of experiments according to the distance between the objects is $d_1=d_2>d_3$

If the angle between the object is less than the angle between arrangement 2, then you can’t be resolved. But the angle between the two objects is equal to and greater than the angle between the objects in arrangement 3. The two objects can be resolved.

Hence, the arrangement in experiment 2 can be resolved.

If the angle between the object is less than the angle between arrangement 3, then you can’t be resolved. Therefore, arrangement 3 cannot be resolved.

Hence, the arrangement in experiment 3 can’t be resolved.