Mirror & Water Images

medium importance~0-1 Q in Tier 11 formulas⚡ 6 shortcuts3 subtopics

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Mirror image of a clock

⏱ 4 min read🧩 5 question types🎯 20 practice Q

The idea in one minute

A clock seen in a vertical mirror has its hands swapped across the 12-6 line. The actual time and the image time always add up to 12:00. So image time = 11:60 minus actual time, and the same rule works both ways.

Why the 11:60 rule works

A clock in a vertical mirror has its hands swapped across the line from 12 to 6. A hand 20 minutes past 12 on the right shows 20 minutes before 12 on the left.

So the actual time and the image time always add up to 12:00.

\text{image} = 11{:}60 - \text{actual}

Writing 12:00 as 11:60 saves you from borrowing. The rule works both ways: actual $= 11{:}60 -$ image.

Examples:

$3{:}45$ gives $11{:}60 - 3{:}45 = 8{:}15$
$10{:}10$ gives $1{:}50$
$7{:}05$ gives $4{:}55$

Rule: Actual time + image time = 12:00.

Special times

12:00 and 6:00 look the same in a mirror. These are the only two such times. Both hands then lie on the 12-6 line.
Times from 12:00 to 12:59: use $23{:}60 -$ time. So 12:20 gives 11:40.
Whole hours: $h{:}00$ gives $(12-h){:}00$ . So 4:00 gives 8:00.
With seconds: use $11{:}59{:}60 -$ time. So 2:25:40 gives 9:34:20.

Reading a clock face

Sometimes a figure shows a mirrored clock with no numbers.

The 12 mark is still at the top.
Read the time the hands seem to show. That is the image time.
Actual time $= 11{:}60 -$ image time.

A hand pointing to the 2 position in the image was really pointing to the 10 position.

Why the hour drops by one

Take 3:45. The hour hand is three-quarters of the way from 3 to 4. In the mirror it is three-quarters of the way from 9 to 8. It is past 8, not past 9.

So the image shows 8:15, not 9:15. When the minutes are not zero, the image hour is $11 - h$ , not $12 - h$ .

Watch: Doing $12 - 3 = 9$ and $60 - 45 = 15$ gives 9:15. That is wrong.

Two-step questions

The mirror shows 4:20. What is the actual time after 1 hour 15 minutes?

First find the actual time: $11{:}60 - 4{:}20 = 7{:}40$ . Then add: $7{:}40 + 1{:}15 = 8{:}55$ .

Convert first, then add. A mirror of a mirror gives back the actual time.

Wrong options to expect

Half-turn time: $3{:}45 + 6{:}00 = 9{:}45$ is where the hands are after a half turn. It is not the mirror image.
Hours mirrored, minutes kept: 8:45 is only half the job.
Borrowing slip: subtracting the hours from 12 instead of 11.

Water image of a clock

A water image swaps top and bottom of the clock face. The hands then point to places that no real time gives.

So exams ask about mirror images of clocks. If a question shows a water image, the clock face is turned upside down, and you read it that way.

Worked example

The mirror image of a clock shows 5:35. Find the actual time.

Actual $= 11{:}60 - 5{:}35 = 6{:}25$ .

Check: $5{:}35 + 6{:}25 = 12{:}00$ . An option of 7:25 forgets to borrow. 11:35 is the half-turn time.

Tip: Always add your answer to the given time. The sum must be exactly 12:00.

Question types you will see

Each type: how to recognise it, the method step by step, and one question to try.

Type 1very common3 practice Q

Mirror time from actual time

How to spot it:

A clock shows a time. What time does its mirror image show?

\text{image}=11{:}60-\text{actual}

Method

Subtract the actual time from 11:60.
Check that the sum is 12:00.

Why it works:

Each hand is reflected across the 12-6 line, so actual and image add up to 12 hours.

Try this

A clock shows 3:45. What does its mirror image show?

Show solution

$11{:}60 - 3{:}45 = 8{:}15$ .
Check: $3{:}45 + 8{:}15 = 12{:}00$ .

Answer

8:15

Type 2common2 practice Q

Actual time from the mirror reading

How to spot it:

The mirror image shows a time. Find the actual time.

Method

Read the time shown in the mirror.
Subtract the mirror time from 11:60.

Why it works:

Reflecting twice gives back the original, so the rule works in both directions.

Try this

A clock looks like 2:25 in a mirror. What is the actual time?

Show solution

$11{:}60 - 2{:}25 = 9{:}35$ .

Answer

9:35

Type 3occasional3 practice Q

Special cases: 12:xx and seconds

How to spot it:

The time is between 12 and 1, or it is a whole hour, or it has seconds.

Method

12:xx: use 23:60 minus the time.
Seconds: use 11:59:60 minus the time.
12:00 and 6:00 map to themselves.

Why it works:

The sum is still 12 hours. Only the borrowing changes.

Try this

What is the mirror image of 12:35?

Show solution

$23{:}60 - 12{:}35 = 11{:}25$ .

Answer

11:25

Type 4common4 practice Q

Mirrored clock face

How to spot it:

A drawn clock, often without numbers, is called a mirror image. Find the actual time.

Method

Read the time the hands appear to show.
Subtract it from 11:60.

Why it works:

The picture gives the image time. The rule turns it back into the actual time.

Try this

A mirrored clock face appears to show 2:30. What is the actual time?

Show solution

$11{:}60 - 2{:}30 = 9{:}30$ .

Answer

9:30

Type 5occasional3 practice Q

Mirror time with elapsed time

How to spot it:

The mirror time is given. The question asks the actual time some minutes later or earlier.

Method

Convert the mirror reading to the actual time.
Then add or subtract the elapsed time.

Why it works:

Time passes on the real clock, so add the elapsed time to the actual time.

Try this

A mirror shows 4:20. What will the actual time be 1 hour 15 minutes later?

Show solution

Actual time: $11{:}60 - 4{:}20 = 7{:}40$ .
$7{:}40 + 1{:}15 = 8{:}55$ .

Answer

8:55

Formula sheet

Mirror time

T_{\text{image}} = 11{:}60 - T_{\text{actual}}

Works in both directions. For 12:xx, use 23:60 minus the time.

Shortcuts that save time

⚡ 11:60 rule

Subtract the hours from 11 and the minutes from 60.

Example

A clock shows 4:20. What does its mirror image show?

Show solution

$11{:}60 - 4{:}20 = 7{:}40$ .

Answer

7:40

⚡ Check by adding

Add the given time and your answer. The sum must be 12:00.

Example

The mirror image of a clock shows 5:35. Is 6:25 the actual time?

Show solution

$5{:}35 + 6{:}25 = 12{:}00$ .

Answer

Yes

Mistakes to avoid

Where most students lose marks on this subtopic.

Mistake 01

Subtracting from 12:00 and slipping on the borrow.

Use 11:60. It needs no borrowing.

Mistake 02

Using the rule on 12:xx times without adding 12 first.

For 12:xx use 23:60 minus the time.

Mistake 03

Mirroring the hours and keeping the minutes.

Both hands swap. Subtract the whole time from 11:60.

Mistake 04

Adding the elapsed time to the mirror reading.

Find the actual time first. Then add the elapsed time.

Mistake 05

Picking the half-turn time as the mirror time.

The half-turn time is the actual time plus 6 hours. The mirror time adds up to 12:00.

Quick revision

Read this the night before the exam.

Image = 11:60 minus actual. Actual = 11:60 minus image.
12:xx: use 23:60 minus the time. Seconds: use 11:59:60 minus the time.
Only 12:00 and 6:00 look unchanged.
Mirrored clock face: read it as it looks, then subtract from 11:60.
Check: given time + answer = 12:00.
With elapsed time: convert first, then add.

Practice: 20 questions

Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.

Topic test · 10 questions

Suggested time 5 min · wrong answers go to your mistake notebook automatically.

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