A one-dimensional model of free electron laser (FEL) has been presented through a computer simulation using Matlab 7.6 program. FEL amplifier with a planar undulator has been considered. The electron beam assumed to be Lorentzian energy distribution. However, oscillator FELs is still impeded by the need for suitable optics. A high gain FEL, on the other hand, requires no oscillator, and can operate in regimes where high quality optics is unavailable. A high gain FEL which requires no input signal, and amplifies the spontaneous emission produced by its own beam is said to be operating in the Self Amplified Spontaneous Emission (SASE) mode. The aim of the project is to study the effects of short wavelengths of laser from the extreme ultraviolet to soft X-ray, and how to obtain small spot size of optical beam. In this work, a study of the electron behavior inside the undulator, the effect of wavelength (λph) in range of extreme ultra violet (10 – 121) nm, and soft x-ray (0.1 to 1) nm on lorentz factor (γ) ,the ponderomotive energy (Up) . The effect of lorentz factor (γ) on velocity component (vz), the electron beam energy (resonant energy), the beta function (β), and finally the effect of ponderomotive energy (Up) on Keldysh parameter (Г). It will be found that peak optical power is very large in the range of Giga Watt and the beam waist of photon beam is very small in the range of Micro meter due to the wavelength of photon radiation (λph). Finally from this study, the beam waist of photon beam is noticed to be very small and it can serve us to obtain a perfect image for tiny sample such as viruses and human member proteins from a single free electron laser shot.