If you're on this page, chances are you have also been subjected to the endless ballad of "theme-based" readings of The Tempest (and likely other literature). While literature essays on drama are a torture within themselves, you should be able to find some use from this breakdown of the themes in the play.
The theme "Power and Authority" in the play will be broken down based on examples of the portrayal of the theme with regards to characters, relationships, and, most importantly, dramatic techniques. Yay.
Power can be described as the possession of influence and sway over someone or something, the ability to control by virtue of possession of this influence. Authority, in the same vein, is simply power one has due to their rank or role in an objective sense, such as in societal hierarchy, or in a another, more subjective sense, like their role in a relationship.
Power and Authority
Reading The Tempest will undoubtedly force you to observe the constant struggle for power that keeps the play in a state of dramatic tension from its initial climactic protasis to its conclusion. The influence of powerful individuals and those below them seeking to grasp this authority for themselves propels the plot forward and creates many of the conflicts observed in the play.
The Tempest's dynamic exists between the group of "powerful" authoritative figures, who rank above the other characters by nature of their relationships or simply by noble hierarchy; and, those without power, simply seeking out every opportunity to usurp those with the authority they desire.
With Power
Prospero
The most objectively powerful in the play, Prospero controls the events on the island with painstaking strategy and caution. His power comes most notably in the form of his "Art," the magical ability which grants him control over the elements of nature, and, therefore, manipulation of every being on the isle. This allows him to discipline his servants, Caliban and Ariel, as well as coerce the courtiers that 'shipwrecked' on the island into the state of mind he needs them to be to exact his revenge.
Apart from his magical ability, Prospero originally held power over his dukedom as Duke of Milan:
"Twelve year since, Miranda, twelve year since, thy father was Duke of Milan and a prince of power."
However, as I'm sure you know, diligent reader, Prospero had been supplanted from this position by a plot led by his treacherous brother Antonio.
Now on the isle, Prospero has power over two servants, though his control of either stems from different circumstances. Ariel was freed by Prospero from a 12-year prison created by Sycorax as punishment for the spirit's non-compliance, and the result is a servitude (presumably in repayment of that debt) to Prospero. Caliban, on the other hand, is forced into becoming Prospero's slave out of the magus' anger at Caliban's attempted rape of Miranda:
"I... lodged thee in my own cell till thou didst seek to violate the honour of my child."
Prospero's "usurping" of Caliban from his self-dominion on the island makes him the ruler of it, gaining power in a way comparably dishonourable to his brother's own coup d'état.
Prospero's magical ability cements him as the top authoritative figure on the island, able to combat the impertinence or undesirable behaviour of his servants. When Caliban curses at him in Act 1 Scene 2, he assures his servant of a terrible punishment:
"For this, be sure, tonight thou shalt have cramps,
Side-stitches, that shall pen thy breath up; urchins
Shall forth at vast of night that they may work
All exercise on thee; thou shalt be pinched
As thick as honeycomb, each pinch more stinging
Than bees that made 'em."
He is further able to dismantle Ariel's puerile prattling for liberty by threatening imprisonment:
"If thou more murmur'st,
I will rend an oak and peg thee in his knotty entrails
Till thou hast howled away twelve winters."
Prospero's authority does not only come through his magical proficiency, but also through the nature of the relationship which he has with Miranda. As her father, he holds not only a deep concern for her, but also the dominion and control a parent has. The use of his paternal authority is observed throughout the play, most notably in his interactions with Ferdinand, with whom the innocent Miranda has fallen in romantic transfixion. He constantly rebukes Miranda's blind advocation for the 'impostor' Ferdinand, commenting even on his daughter's backwards counsel:
"O dear father, Make not too rash a trial of him, for He's gentle and not fearful."
"What, I say, My foot my tutor?"
Alonso
The King of Naples, Alonso is the highest ranking noble in the play. His position in the Neapolitan hierarchy makes him the authority figure targeted by Antonio and Sebastian for their murder scheme and targeted by Prospero for the return of his dukedom. Alonso's authority is more evidently recognized by others, and he comes off as less of a leading character in the play- though that is indubitably influenced by the loss of his son, which results in his grief-stricken stupor for the greater duration of the play.
However, while Alonso's laconic nature triggered by perceived loss is evident in most of play, his authority is undeniable in specific moments, such as when he returns Prospero's dukedom to him out of remorse in Act 5 Scene 1:
"The dukedom I do resign and do entreat thou pardon me my wrongs."
The duchy at that point had lain with the perfidious Antonio, but Alonso relinquishes it in that moment without any need for consultation with him, nor with any complaint.
Without Power (And Seeking It)
Antonio
The traitorous Antonio is the first character in pursuit of power audience is told of during Act 1 Scene 2. In this scene, Prospero is relaying the events that led up to his ousting from his dukedom, Milan- and Antonio is presented as the main villain of the story. Prospero had lavished his trust on his brother, tasking him with most of the administrative duty of the duchy while he pursued "the bettering of his mind." Then being below Prospero in rank, Antonio's desire for power drove him to collude with the King of Naples to "extirpate" Prospero from the dukedom and take the position of duke for himself.
His dryness "for sway," as Prospero puts it, is one of his main characteristics presented in the play.
However, it seems that this power is not as complete as Antonio truly desires it to be, as he still pays homage to the king due to the subjection of his coronet to the crown. In the play, being apparently always bent on seeking his own benefit and ascension regardless of the morality or ethicality of the means, Antonio sees the opportunity to kill the king in his slumber and ascend Sebastian to the monarchy instead. Through this, he would gain the new king's favour and freedom from the homage he agreed to pay. His depraved ambition, like a contagious disease, he attempts and successfully spreads to Sebastian, who is like-minded but doesn't appear as inherently corrupted as his compatriot. Agreeing on the murder of Sebastian's own brother displays more of his desire for power, even if it is only sway with the king and freedom from homage.
Sebastian
Sebastian's desire for power is ignited by Antonio's coaxing in Act 2 Scene 1, where the two are serendipitously left awake while the rest of their party is charmed into slumber. The usurping duke convinces him "what a sleep were this for your advancement," persuading him to take the opportunity given by the king, his brother's, sleeping. He is prepared to take his brother's life for the promise of the position of king (though, it is ironic their struggle for this power, since monarchy would be meaningless if they truly are stranded on an island far from Naples).
Caliban
Caliban's desire for power comes from a place of feeling wronged. The newcomer Prospero, to whom he showed such kindness and hospitality by familiarizing his visitor with the island ("and then I loved thee, and showed thee all th' qualities o'th' isle"), ends up taking over the island and even enslaves him, taking both his birthright and his freedom in one fell swoop.
"This island's mine, by my mother Sycorax, which thou tak'st from me."
Caliban wants to be freed from Propsero's rule, and believes that the island is rightfully his. However, the approach taken by Caliban in reclaiming the isle and freedom is highly paradoxical. Taking Stephano, a drunken butler, as his king and kneeling to him, he essentially only transfers his servitude from Prospero, his current lord, to Stephano. Although the butler promises to make Caliban his "lieutenant, or {his] standard," Caliban offers the same services of wood-fetching and fishing to Stephano as he currently does to Prospero. It is from this backwards/self-contradictory approach that it can be inferred that Caliban desires Prospero's donwfall due to a vengeful spirit and his current lack of power. It should be noted, though, that Caliban holds power over Stephano and Trinculo in his ability to persuade them into this plot. This plan is essentially his bidding, and although it would end up benefitting Stephano most (if it were to come to fruition), Caliban would technically achieve his goal of destroying the 'tyrant' whom he so hates.
Relationships between those with power and those without it
Prospero and Ariel
The relationship between the master, Prospero, and his servant, Ariel, is mutually respectful, and often affectionate in the master's frequent commendation of his 'tricksy' and 'dainty' spirit's work mirrored by Ariel's enthusiasm. Ariel's alacrity and commendable precision in carrying out Prospero's commands show a willingness in service that forms a foil to the magus' more aggressive relationship with Caliban.
Although their relations are frequently without difficulty or reluctance, Prospero still threatens Ariel with imprisonment when the spirit expresses impatience with his 'liberty' as promised by Prospero. Ariel's response is very deferential in tone and seems to hint at truly submissive regret:
"Pardon, master,
I will be correspondent to command
And do my spriting gently."
Though his promise at the end of their interaction indicates freedom within two days, Ariel is actually freed within three hours.
As previously stated, Prospero regularly commends Ariel's work in completing his bidding. He praises the spirit's faithful creation of the tempest and his subsequent placing of the courtiers throughout the isle, and again extols Ariel's performance as a harpy condemning the 'three men of sin' in Act 3 Scene 3.
Prospero and Caliban
Caliban and Prospero's relationship is one of mutual resentment, where either party feels wronged by the other, inspiring a vitriol in all of their interactions. Caliban, as discussed previously, feels wronged Prospero for having squandered his kindness in showing him the isle by enslaving him and confining him to a rock, unable to enjoy the isle that is his birthright. Prospero sees as alternative view of this, however; the savage, 'freckled whelp' Caliban is undeserving of kindness, an inherently corrupted being "whom stripes may move, not kindness" because of his attempted rape of Miranda. Because of this impasse, where both men see the other as a villain taking advantage of their own kindness, their hatred of each other seems to remain at the forefront of their interactions.
Caliban's first line in the play is actually a curse directed at Prospero and Miranda ("as wicked dew as e'er my mother brushed, with raven's feather and unwholesome fen drop on you both"). He views the magus as a tyrant, despising how easily he sets his spirits upon him "for every trifle." This motivates him to seek revenge on Prospero, colluding with Stephano and Trinculo to kill him and claim the isle.
Dramatic Techniques Portraying Power and the Pursuit of Power
Aside
"I must obey. His art is of such power that it would control my dam's god Setebos."
Caliban's acknowledgement of the god-like potency of Prospero's art justifies the precedent of his unconditional obedience. This power Prospero has forces him to suppress his rebellious nature, as the magus is definitely capable of plaguing him with all the "old cramps" and aches he threatens with, and more. Prospero is aware of the effect his power has on his slave, hence why he remarks that "stripes may move [Caliban], not kindness."
"My high charms work, and these, mine enemies, are all knit up their distractions. They are now in my power..."
At this point in the play, Prospero has held a firm grip on every event in the play; driving each of the trio who usurped him to near madness, while manipulating their beliefs and guaranteeing the outcome he desires. "They are now in [his] power," all in a stupor induced by Prospero's magic and the guilt he attempted to evoke in each of them with the magically events sprinkled throughout the play.
Dramatic Irony
When Antonio and Sebastian are about to kill the king, they are interrupted by the king's awakening (by Gonzalo, who was awakened by Ariel at Prospero's behest). This results in a somewhat comedic sequence (which also carries an amount of tension) where the two villains fabricate a story about hearing "a hollow burst of bellowing" to conceal their true intentions. This frantic recount of "a din to fright a monster's ear" is dramatically ironic, in that the audience and the co-conspirators are aware of the lie, yet the rest of the Neapolitans are (at least ostensibly) oblivious. The significance of this in portraying the quest for power is that it reveals the morally depraved depths to which people (specifically Antonio and Sebastian) will go in order to come by power. Their attempt to conceal the truth in this ironic scene shows a shared mendacious nature bent on ascertaining influence in any way possible; flaunting a lack of conscience when the others sleep then trying to appear righteous before them in waking.