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I was drawing a spacetime diagram to relate Doppler shift effect but i stuck at a point which i can't understand

This is what I'm trying to draw

An object with mirror is moving away from me with a velocity of 50% speed of light

When each second passes in my clock i send light pulses at that object.

I sent 4 light pulses in 4 second.

The object starts when t=0 in my clock

When t=1 in my clock that object will be ’half light second away’ at the same time t=1 i sent my first light pulse. So in my clock the first light pulse must hit the object when t=2 in my clock (when t=2 in my clock the object will be 1 light second away)

When t=2 i sent my 2nd light pulse and it must hit the object when t=4 in my clock

When t=3 i sends my 3rd light pulse & it must hit the object when t=6 in my clock

Finally t=4 i sends my 4th light pulse and it must hit the object when t=8 in my clock

So i draw my spacetime diagram and drew a 22.5 degree angle, it will be 50% speed of light

In each seconds i sends a light pulse, so i drew it in 45 degree angle.

But the intersection of light pulse and speed of the object doesn't match with time in my graph

The first light pulse which i sent should intersect at t=2 in my graph but it intersect only below 2 second.

So if i try to adjust the graph inorder to reach at t=2 the angle changes and it will increase the speed of the object. This is like the same for all 4 light pulses

I know moving objects contract in length, but this isn't that

I also know time slows in moving object, but i don't need to care, i need my spacetime graph to be correct, they may receive it in different times

If it is my mistake help me to find it.

The picture is below

http://www.flickr.com/photos/sreenath666/10286909563/ [Broken]

This is what I'm trying to draw

An object with mirror is moving away from me with a velocity of 50% speed of light

When each second passes in my clock i send light pulses at that object.

I sent 4 light pulses in 4 second.

The object starts when t=0 in my clock

When t=1 in my clock that object will be ’half light second away’ at the same time t=1 i sent my first light pulse. So in my clock the first light pulse must hit the object when t=2 in my clock (when t=2 in my clock the object will be 1 light second away)

When t=2 i sent my 2nd light pulse and it must hit the object when t=4 in my clock

When t=3 i sends my 3rd light pulse & it must hit the object when t=6 in my clock

Finally t=4 i sends my 4th light pulse and it must hit the object when t=8 in my clock

So i draw my spacetime diagram and drew a 22.5 degree angle, it will be 50% speed of light

In each seconds i sends a light pulse, so i drew it in 45 degree angle.

But the intersection of light pulse and speed of the object doesn't match with time in my graph

The first light pulse which i sent should intersect at t=2 in my graph but it intersect only below 2 second.

So if i try to adjust the graph inorder to reach at t=2 the angle changes and it will increase the speed of the object. This is like the same for all 4 light pulses

I know moving objects contract in length, but this isn't that

I also know time slows in moving object, but i don't need to care, i need my spacetime graph to be correct, they may receive it in different times

If it is my mistake help me to find it.

The picture is below

http://www.flickr.com/photos/sreenath666/10286909563/ [Broken]

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