Concept:
The given sentence is an imperative sentence. Imperative sentences are used to express commands, orders, requests, instructions, advice, or suggestions. In such sentences, the subject “you” is generally understood and remains hidden.
When an imperative sentence containing an object is converted from active voice to passive voice, the focus shifts from the person performing the action to the object receiving the action.
The standard passive structure for imperative sentences is:
\[
\text{Let} + \text{Object} + \text{be} + \text{Past Participle (V}_3\text{)}
\]
This structure preserves the commanding nature of the sentence while changing the voice.
Step 1: Identifying the components of the active sentence.
The given sentence is:
\[
\text{Open the door.}
\]
Its grammatical components are:
• Implied Subject : You
• Verb : Open
• Object : The door
Since the sentence contains a direct object, it can be converted into passive voice.
Step 2: Applying the passive voice formula.
Using the standard imperative passive structure:
\[
\text{Let} + \text{Object} + \text{be} + \text{V}_3
\]
Substituting the appropriate words:
\[
\text{Let} + \text{the door} + \text{be} + \text{opened}
\]
Thus, the passive form becomes:
\[
\text{Let the door be opened.}
\]
Step 3: Evaluating all the options.
• Let us open the door.
This sentence expresses a suggestion involving a group and remains in the active voice.
Hence, it is incorrect.
• Let the door be open.
Here, “open” functions as an adjective rather than a past participle verb.
The passive structure requires the past participle “opened.”
Hence, it is incorrect.
• Let the door be opened.
This follows the exact passive voice formula for imperative sentences.
Hence, it is the correct answer.
• The door may be opened.
This changes the meaning from a direct command to a possibility or permission.
Hence, it is incorrect.
Step 4: Final verification.
The sentence retains its imperative nature and correctly shifts emphasis to the object receiving the action.
Therefore, the correct passive voice is:
\[
\boxed{\text{Let the door be opened.}}
\]